Square Dancing Now Forward Again With a Right Hand Swing

Hexagon Squares

Clark Baker, September 2002

Abstract

Square dancing is usually danced past 4 couples who start each sequence in a square germination. This newspaper describes how 6 couples tin can offset each sequence in a hexagon formation, and trip the light fantastic the aforementioned choreography with the same timing every bit the usual foursquare. Certain dancers will enjoy this twist on square dancing.

Introduction

Hexagon squares are the next in a serial of Square Games. Each is a global twist on normal square dancing which can be danced in real time while the caller is calling to the rest of the floor.

In March 2002, I created a new square game, Hexagon dancing, which requires 6 couples. A history of Hexagon Squares and similar variations can be constitute in the Appendix.

The Nuts

I am going to explain the basics by telling you how to walk an bodily Hexagon set up through the nuts. I propose yous do exactly that, or follow this in your head, on newspaper, or with checkers.

Arrange 6 couples in a perfect hexagon. At that place should be two couples lined up on walls (the couple with their backs to the caller and the couple they are facing). The other four couples are non lined upwardly on walls.

Starting with the couple with their backs to the caller and going around the set in promenade direction, identify each couple every bit heads, sides, heads, sides, heads, and sides. Have the heads raise their hands. Have the sides raise their hands. Point out that the couple directly across the hex from them is not the same as them (i.eastward., opposite every head couple is a side couple!).

Heads Go Forwards And Back. Discover how the person they approach when going forward is not directly facing them, but slightly effectually the corner from them. This kind of slightly around the corner will happen a lot in Hex dancing.

Heads Go Frontward again and Foursquare Thru 4. It should feel like a wrong way grand in a circle of six. Don't worry about the angles and turns. With any luck, all heads will end facing the sides. At this point the unabridged set looks like a "Y". This will be very mutual.

All Do Sa Do To A Wave. Whenever we do 4-dancer calls on the exterior (which is very common in singing calls), nothing special happens in the Hex square. We just work in our ain group of 4. To see this, dance the following: Swing Thru, Boys Run, Curve The Line, Correct And Left Thru, Dixie Style To A Wave, Merchandise The Wave, Centers Run, Centers Swivel, Diamond Circulate, Flip The Diamond, Centers Trade, Swing Thru.

At present we should nonetheless be in waves with boys on the end. Notice how the whole set looks like a Triangle (or a delta). But one of the iii sides can be lined up on a wall. The ends of each wave are boys. They must be careful to not touch or get too shut to the adjacent wave. Information technology would exist easy to agree hands from one wave to the next, but this would be very incorrect.

Let'due south talk about each wave. The dancers who are looking out are just like the dancers looking out of any wave. They should know where to go along a Broadcast. Consider the end looking in. On a Broadcast, he volition move to the next wave, following a back, moving around a slight angle, and terminate every bit an end looking out. Have all the Boys Broadcast. Take all the Boys Broadcast once again. Now the girls plough. The girl looking in is too following the dorsum of some other girl in the next moving ridge. Have the Girls Circulate, then Circulate once more. Exercise a Swing Thru to movement everyone into new positions and do some more than Circulates and Acey Deuceys. Have the Centers Run and do two Couples Circulate.

At this point, y'all should cheque out some animated illustrations created by Justin Legakis. The "Square/Hexagon Animation Gallery" will show you several of formations, and "Hexagon Formation Animations" volition testify you a variety of calls. If your calculator has Macromedia's Flash Player yous should besides check out these animations by Yoichi Shinohara. If your browser has Coffee and JavaScript cheque out TAMination. Finally a video which starts with a teach of broadcast and concludes with a singing call. This was taken at the SCVSDA's 49th Jubilee, Oct 2005, in San Jose.

Plus Calls (and Mainstream) that requite problem

I thing I accept noticed is that Hex dancing tin can evidence up weaknesses in how dancers take internalized their knowledge of the calls. Sometimes you can become through certain calls by feel, by floating (and having people guide you lot), or by walking a path without knowing the underlying rule. In certain cases the Hex shape will take those methods of dancing away and exit y'all loftier and dry.

From a squared set, Heads Laissez passer The Ocean. This is hard for several reasons. First, the adjustment from a squared set to having the heads be facing couples in the middle is so automatic that we get lost doing it in a Hex square. Having the Heads Become Forward and Dorsum helps identify which dancers are facing. Next, we commonly dance Pass The Body of water by feel. In this case, the Hex result removes that ability. We must exercise it by definition. Heads Upwardly To The Heart and Pass Thru. Discover a new partner. Face up That Partner. Step To a Wave With That dancer. The center half-dozen should have 3 mini-waves, and the head women have a 3-dancer left hand star in the heart.

Have the Heads Swing Thru (right paw half, left hand star ane/3). Have The Heads Swing Thru once again. Nosotros are in a 1/iv Tag. Two good calls from here are Extend and Ping Pong Circulate. Everyone Ping Pong Circulate. Centers Swing Thru, Double. Extend. Nosotros should now have normal waves.

Relay The Deucey is actually cool. Look at where you are in case we break down and have to go back. Look at who yous are holding onto. Just like a real Relay The Deucey, you volition cease up with this dancer. Go by parts. Turn one/2 Correct. Men left three/4, ladies walk a little effectually the outside. Daughter On. Stop.

Nosotros should have the following. 3 waves of 3 joined in the center in a correct-mitt star of 3 boys. 3 loose women on the outside. These women must not get too shut to the star of boys or they volition get sucked in. Instead of the women thinking that they walk downwards the "Y" and up an arm of the "Y", they should focus instead on walking around the exterior of the set. Their adjacent human action will be to get "on" the tidal wave. They should exist looking for where that is.

OK, turn 1/ii by the Right (1/3 in the very heart). Boy off and girl on equally the others turn one/2 past the Left. one/2 Right (1/three in the very eye). Boy off, as the girls turn 3/iv past the left. The boy who is walking effectually the outside at the terminate and will become the pb end of the wave has a tendency to go also far (which is also true in normal squares). Brand sure he stops sooner. Practice the telephone call several times from the same and the other position.

Spin Concatenation The Gears is the easiest of the "big" calls. Outset from normal waves. All turn 1/ii. Boys 3/4 while the girls plow back. Center three boys observe a right-hand star and plow it 1/3. Each 4-dancer star turn left 3/four. iii girls star i/iii in the very center. Girls left 3/iv while the boys turn back. This is ordinarily successful but it is important to get practice looking for the various parts. Some dancers are dislocated by the stars on each side, the star in the center, who they are working with, etc.

Spin Chain And Commutation The Gears is also piece of cake. Everything is the same until the exchange point. The lady who leads her star just has to caput in an judge location and brand the wave. The whole set will gel into a Triangle of 3 waves.

Track 2 is tough. From a Squared Set, Heads Star Thru. Double Pass Thru. Focus on this: Every boy is going to become a girl with his right manus. Somewhere close past, nosotros should have right hand waves with girls in the centre. If these two weather condition are met, we are close enough. Now, starting time the Track 2. Boys go around the girls and down the side and get some new girls. Every male child get a girl. Which girls take left hands with each other? No one is in the very eye of the prepare. We should have 3 normal ocean waves.

We recently got tricked by Triple Scoot. The #3 dancers in the columns will star with each other. Each dancer skips the get-go clump of dancers they run into and joins the next clump. Coordinate has the same center result and was as well took some exercise.

From a squared set, Sides Face, One thousand Square. I ordinarily don't walk this — it just works! Encourage everyone to take one step for each beat of music. Since the Hex foursquare is a little larger than a normal foursquare, in that location is less a trend to blitz. This looks and feels actually absurd.

Teacup Chain. This 1 is a existent problem. It is hard to practise and has few rewards for doing it correctly. To make the timing work, we demand to retrieve of it every bit skipping dancers instead of progressing around the foursquare in a nice order. Here is how it goes. Side men always fetch women from the heart and send them to the next caput men. Head men ever receive women from the side men and transport them into the center. When the head women go into the center with a right arm, they star to the third man. When they go in with a left arm, they star to the fifth man. This volition cause a weird progression, but it times out properly.

Fast calling, specially when the centers are activated, can be tough. Heads Pass The Bounding main, Swing Thru, Extend The Tag and nosotros are dead. Same goes for Laissez passer To The Center, Pass Thru. If you are dancing patter for the first fourth dimension, expect to intermission downwards and have a plan. The plan is to foursquare your set and make lines by having the heads turn slightly to the right and sides to the left (every bit couples) and go forward and back. The caller will get to lines to pick up some other broken square soon enough.

Memorized sequences with clever choreography can be difficult. From normal lines facing, Touch 1/iv, Circulate 1 1/two, Centre 6 Trade and Curl, Center 6 Slide Thru, Left Allemande. The heart three dancers working around the flagpole center for any call (e.one thousand., Slide Thru, Pass Thru, Dosado) is unusually difficult.

2-Couple Practise

While not as much fun, you tin can exercise some stuff with 3 couples dancing ii-couple fabric! It is hard because the "Y" vs. Triangle result comes upward at every call. From facing couples (a triangle) your partner is beside you but the dancer you are facing is not direct in forepart of you lot. If you adjust so that the dancer you are facing is directly in front end of you (a "Y"), now your partner is not directly beside you. Your partner is in a slightly "bent" couple with you.

I ordinarily kickoff with a few Right And Left Thrus, a Ladies Chain (to bring upwardly the star 1/iii result) a few Flutter Wheels (girls get a new man and bring him to a place neither of you have been to), and a Foursquare Thru. Then exercise some box calls (Box Circulate, Walk And Dodge). Don't forget diamonds (from waves, centers run, new centers swivel (dancers will usually turn too far on a Hex Swivel — you may need to dorsum them up slightly to get an exact diamond), check a diamond). Diamonds look really funny, and not at all like a diamond.

Really hard calls are Fan The Top, Scoot Back, and Cycle Thru. As well keeping track of which dancers "own the wall" (i.e., should be lined up on a wall) is actually hard. I find it useful to keep runway of who "owns the wall" with iii couples, merely not for 6. With half dozen couples, everything just seems to work.

3-couple dancing is also useful when you lot want to show the Hex stuff to someone but don't want to detect 12 interested people. I accept never danced the 3-couple stuff live with music. Non-symmetric material does not piece of work so don't get trapped with it.

Hexagon Summary

All symmetric choreography works. Some may be very difficult.
Trip the light fantastic toe so that the timing is the same every bit in normal squares.
When you work in the very middle, under achieve (turn 2/3 the usual amount).
The shape of your prepare will usually be either a "Y" or a Triangle.
You can transition betwixt "Y" and Triangle as needed.
Each 4-dancer telephone call volition take you lot naturally stop in a "Y" or Triangle.
Go 4 hands on Right And Left Grand and Promenade the next dancer.
Promenade to the nearest home position of your blazon.
Have fun.

Teaching experience

I accept had the opportunity to lead and dance Hexagon squares over 20 times so far. Normally I get a square past itself and work with it for about x minutes. And so we get into the back of the hall and trip the light fantastic at least 2 tips and sometimes every bit long as 2 hours. While nosotros aren't keen at showtime, the learning curve is steep. This means that a little practice yields great gains and makes you lot want to go along doing it. Each new phone call you lot accomplish (Load The Boat, Relay The Deucey, Grand Foursquare) gives you more rewards. The fact that you lot broke down on Pass The Ocean doesn't seem similar much of a setback.

I try to choose dancers who I believe will enjoy the experience. Usually this means people who have skilful trip the light fantastic skills, who have been dancing a while, possibly who know Advanced or Claiming, who have adept recovery skills, and who have shown a by involvement in doing different things with their dancing.

No matter how we form the set, at that place are usually one or two dancers who clearly aren't getting information technology, or whose trip the light fantastic skills were already weak and this has pushed them over the edge. Since these dancers have already spent the time getting trained, I but go on them in the square. Sometimes they catch on, and ordinarily they don't cause a lot of bug. After several tips, it is good to give those that would like a break a chance to escape. Usually there is someone on the sidelines who has been watching and would love the opportunity to bring together the foursquare. If they take been watching, they don't need whatever instruction.

While I would prefer to spend 10 minutes or so explaining the footing rules and walking people through the various calls, in one case we had no time for that. Three experienced Hex dancers squared up (as heads) with 3 couples who had never done it before and had no idea what was going to happen. The music was already going and the callers were calling with no breaks at an afterward party. I believe I squared the states up, identified heads and sides, said that we were going to dance what he was calling, that we become 4 hands on a right and left grand, and we wouldn't necessarily promenade to our original home, and to sentry u.s.a. and become with the menstruation, and not to worry.

With basically no instruction, we did ok at first and got better. Each time we broke down on something we would square up and if I had time, I would quickly explain it or walk it. Soon nosotros switched ane head and one side couple so when the sides were asked to do something, at to the lowest degree 1 couple had done information technology before. In a few tips we were doing fine and having fun. Soon one experienced couple had to get out and was replaced by a new couple who had been watching on the side. Nosotros still did fine.

One fashion to learn Hex dancing is to watch a square doing it, and so jump in. Another fashion is to put ane or ii new couples in an experienced square have have them become with the menstruum.

No matter how the Hexagon is formed and trained, information technology helps to have a leader. The leader signals when promenades stop. The leader decides when the hex is broken downward and asks it to "square up". Also, after squaring up, the leader watches the other squares and decides when to "make lines". Past making lines, the hex will get a lot more than practise dancing. Finally, when there is down time (say they are changing callers), the leader should walk the last few calls that broke the hex down (and then information technology won't happen again).

Observations

Ane could put 8 couples in an Octagon and do the same thing. I have never done this. The angles become even worse so dancers you lot are "facing" are really around the corner by 90 degrees. I am not sure the hurting is worth the gain.

In a normal square every dancer has a diagonal contrary. In Hex squares every dancer has 2 opposites. Instead of being beyond the square, each is down one arm of a "Y". The dancer who is downwardly to his right will always be down to his right. While "following your opposite" tin can exist a useful tool in normal dancing, I have establish it to be useless in Hex dancing. The only time I discover my opposites in on the promenade when I am watching the square to run across when we will stop. The contrary to my right is always ii couples ahead of me on the promenade.

In normal squares in that location are ii sequences of couples — in and out. Promenade home only works when you lot are in sequence. In Hex squares there are 3 sequences of couple, just ane of which is truly "in sequence". This doesn't matter to usa considering we only promenade to a home position of the right blazon (head or side) instead of our original home. If your goal was to phone call only to Hex squares and to resolve, and then the three sequences would matter and you would take to go information technology correct.

From a Double Pass Thru germination, you can retrieve of a normal foursquare as having your half the square and the other half the foursquare on the other side. In the Hex situation you still have your half, simply someone put a beam splitter, mirror, or prism in the heart of the square which has duplicated the far half and moved one re-create to the left and one to the right.

There are 6 sex arrangements for each formation in normal squares. The same holds for Hex squares. Every symmetric germination in normal squares has a respective formation in Hex squares.

If the normal square resolves, the hex square volition get the heads together and sides together, merely sequence and partners may be incorrect.

Consider a call from facing couples in which the left side dancers right-pull past with each other. Consider the aforementioned call, simply the left-side dancers utilize the other hand and left-pull past with each other. In normal foursquare dancing both version of this phone call would have the same effect. However, in Hex dancing the two versions would have different effects! In Hex dancing the traffic pattern matters. This means that all choreography programs which know definitions of calls but not traffic patterns (which I believe is all of them) volition non exist able to trip the light fantastic Hex with their existing database, even if their display software is updated for the odd angles and extra couples.

In a conversation with Justin Legakis we discussed that one could write a calculator program to automatically convert animations of 4 couple squares to Hex annimations. He has done simply that and you can meet the results hither. Click on the "2-Couple, Square, Hexagon, and 8-Couple Generalizations".

One dancer commented to me: If yous recall of foursquare trip the light fantastic calls executed in a normal square in terms of fractions with a denominator of 4, for example, Right And Left Thru would move y'all 2/4 the way across the square, that tin be transformed into hexagon-ese past changing the denominator to six, but keeping the same numerator. So, Correct And Left Thru moves you 2/vi (or 1/3) of the way effectually the hexagon. But of grade, this transformation but applies to operations that either motion through the center of the formation or touch the unabridged formation with respect to the centre (does that make sense?). Information technology probably complicates things too much to exist explained simply, but it does quantify what yous were referring to as "under-achieving". In a sense, it'southward more or less a unlike way of maxim "yous skip the same number of people (or positions) you would skip in a normal square".

In e-mail service to me, Justin observed:

You mention several times that the equivalent of a 2x4 looks either like a Y or a triangle, and then when dancing you must be ready to adjust between these shapes. I prefer to call back if it as 1 formation, with curved waves (or columns) so you meet the iii 1x4s, and the three 2x2s at the same time. Of course, this is how I've idea about Hexagon Squares on paper — I don't take your experience with dancing it.

With care, one can write choreography which works (i.e., resolves to correct partners, and in sequence) in both normal and Hex squares at the same time. While interesting, I don't think it is worth the effort.

Walls: While dancing Hex, one normally doesn't think of facing "Head Walls" or "Side Walls" even though these terms definitely apply in normal squares. Noriko Takahashi clued me into thinking almost this. When the role of the hexagon which is lined upward with the walls in the room is close to the caller, anybody is facing head walls. When the part of the hexagon which is lined upwardly with the walls in the room is far away from the caller, everyone is facing side walls. No one should ever face the real side walls in the room.

Sight Calling Hexagon Squares

If the entire hall is hexagon squares (peradventure because the unabridged hall is only 6 couples), then a caller might be tempted to call to this square. If this were the case, I would make several changes in the rules.

Right and Left G is vi hands
You will go your partner and promenade to your home position
Use proper fractions (Heads Ladies Chain 1/3, 2/3, etc.)
half dozen Ladies Promenade Inside, Get Back Abode (actually goes all the manner around)
Teacup Concatenation, middle ladies turn so as to progress, activeness repeats 6 times. Exist aware that information technology ends turning partner by the right and so the caller must direct an appropriate next move.

Hex with these rules should represent to how Clay Goss uses it in his exhibition dancing, how Nib Eyler uses information technology at festivals, and probably to how Lee Boswell intended information technology. See Bill's paper hither.

Sight calling to such a square is easy. That is, picking calls that are legal and flow well is piece of cake since you just have to call your usual combinations. Sight resolution is some other matter.

Developing a method of sight resolution that works, is not likewise difficult to learn, that can be used without any long pauses, and that doesn't have as well many calls is difficult. For those interested in such things, I call back trying to develop a Hex resolution organization is a great exercise. For many of us, sight resolution systems came to us fully adult. They are presented as an algorithm that we have to memorize and follow and later we will be able to aggrandize on the organisation. In Hex y'all have to outset from scratch. I recommend thinking near each alphabetic character in FASR and what it means in Hex. Consider also that from a Beginning Double Pass Thru with the ends paired and the centers unpaired nosotros would unremarkably phone call either Laissez passer Thru or Square Thru 3. In Hex we would take Pass Thru, Square Thru 3, and Square Thru five. Also, in Hex, the partners don't stay with you when the centers Pass Thru.

If yous come up with something, let me know. If I effort my method and it works, I might mail service information technology here.

Tomas "Doug" Machalik (Czech Republic, Europe) has a interesting website which has an commodity on the Sight Resolution of Truthful Hexagons.

P.South. I take recently learned that Bill Eyler has been using Hexagons for about 16 years and sight calling them to regular dancers for nearly the concluding 10 years.

Decision

I have had a lot of fun with Hexagons. I can't get enough floor time with them and haven't yet gotten bored. At that place always seems to exist something new and unexpected effectually the corner (e.g., Ferris Cycle, centers Veer Left, Veer Correct).

Hexagons are not for everyone. If yous present this gimmick to everyone, a piffling chip goes a long mode. Probably many people would merely as soon not dance Hexagons at all. For those that do enjoy them, in that location are many hours ahead of new-found fun with our existing calls and choreography.

I welcome feedback, corrections, and suggestions on this paper. Besides, if you teach or trip the light fantastic Hexagons I would exist interested in hearing your experiences. Please write. If y'all take any questions on how certain calls should work, just inquire. I e'er accept an stance.

My experience with Hexagons is relatively new. While I have been dancing since 1974 and they were invented in 1968, I hadn't encountered them in any depth earlier talking with Clay in 2002. If you have other history or credit which I should know about (eastward.g., "Back home, Joe has been doing that stuff for years. Except, he does it slightly differently than what you say..."), please tell me.

Clark Baker
email: cmbaker@tiac.net
phone: (617) 484-0175

Appendix

History

The booklet "Choreography Gimmicks" by Will Orlich (bachelor from American Squaredance Mag) has a section on multiple squares with the following entries:

Progressive / Exploding Squares
Hexagon Squares, Jim Gammalo, 1968
Triangle Squares, Lee Boswell, 1968?
Mini-Squares (Two-Couple Squares)
Kaleidescope Squares, Gloria Roth, 1974 (4 squares 1 behind another)

Jim Gammalo's Hexagon squares are vi couples in a rectangle with 2 couples at each of the heads and one couple at each of the sides. As I said above, this is very popular with callers, simply not what I mean by Hexagon Squares.

In The Handbook of Modernistic Square Dancing, Jay King describes Lee Boswell'south Triangle Squares by saying that they start in an actual hexagon with the couples alternating heads and sides and that each sequence starts with heads or sides leading to the right and circling to a line. This gives 3 lines (each side of a triangle). If you lot curve the line, the set is in a "Y" shape. While I have no other information on how Lee Boswell used his Triangle Squares, they are exactly what I am talking about.

Beak Eyler wrote an commodity in the May 1993 issue of Mikeside Management (a caller note service) entitled "Apple PIE" DANCING; Hexagons - A Fiddling Slice of Square Trip the light fantastic toe Sky. Nib says that the July 1986 outcome of American Squaredance Magazine featured an article on the concept of Triangle Squares by Ross Crispino, with credit to Harriett Miles. Bill has been using Hexagons in operation exhibitions for 16 years and as an entertainment tool at dances and festivals for the final 10 years.

I have e-mail from Dan Koft from May 2000 on the subject area of gimmicks. Rutgers Promenaders has i "Unusual Mainstream" tip each evening and one of the tips was "True Hexagons (3 even couples, iii odd couples, Square thru vi to go to corner)". I don't know where Dan first saw this formation or what choreography he used. In talking about gimmicks he did say that True Hexagons were not worth the prep time. I am not sure if he is saying that it took a lot of effort to ready cloth that works, or if it takes too long to teach dancers how to dance in a hexagon.

At Callerlab in March 2002, Clay Goss introduced me to the Hexagon Squares he uses with his exhibition group, the Clay Figures. They dance in a true Hexagon (heads, sides, heads, sides, heads, sides) and brand utilize of several of the viii-dancer Plus calls (eastward.m., Relay The Deucey, Load The Boat). I was total of questions and he explained how Double Pass Thru, Grand Swing Thru and the diverse Ladies Chains worked. While someone had tried to show me choreography from a Hexagon in the past, it wasn't until I talked with Dirt that something started to click.

Soon afterwards I left Callerlab I realized ii things:

Every call used in MWSD tin be "extended" to a Hexagon
A Hex square can dance while the real caller is calling to a normal foursquare

One evening, I was able to grab 6 couples of Tech Squares dancers and we spent an hour walking diverse calls from a Hexagon. I didn't take a precise explanation of what the rules were, and several in the group were resistant to only "proceed with the flow" and see what happens.

At the New England Convention in April, we were able to go a Hex square and actually try dancing to a live caller. We started with some trepidation, and we had a few breakdowns, but we danced two tips with great success. Anybody was very enthusiastic and thought it was bully how the diverse calls like "Heads Foursquare Thru" just worked out even though the angles are all weird. Also, the "look" and "feel" of certain calls really changes, which added to the magic.

I have shown Hex dancing to challenge groups in Chicago, Scarlet Ridge, L.A., and Ploen, Germany, and have danced it at the National Convention in St. Paul (and every National since) and the Singles convention in Richmond. We have recently danced information technology for the commencement time at a regular Tech Squares dance. I have presented it at Callerlab in 2003, 2004, and 2005.

In 2005 I struck upwards an e-mail correspondence with Colin Hume (a Folk Trip the light fantastic caller and composer in England) and mentioned Hexagons. He has written a traditional "square" in the Hexagon mode. You can observe it here.

Since 2003, Hexagons have been receiving increased exposure, including at National Conventions. The handout used by Doug Davis and Nasser Shukayr in 2005 is available here.

Every bit mentioned above Nib Eyler has been using Hexagons successfully since he first read about them in 1986. His writeup us available here. Bill'southward Hexagons have some differences from those I have but described. When information technology is necessary to distinguish the two, we call his Western Hexagons and mine Eastern Hexagons.

Western Hexagons — the entire room is asked to "Hex Upwards". The caller explains the groundrules and proceeds to call choreography which will become everyone back to their original partner. Often the caller will alter the calling terminology to reflect the fact that anybody is in a hexagon (e.g., Vi Ladies Chain 3). Sometimes the caller will introduce variations on existing calls (eastward.grand., Grand Triangle) which don't fit the rules of Eastern Hexagons. The goal is to entertain everyone for a tip or an 60 minutes without too much teaching and without everyone having to think likewise hard.

Eastern Hexagons — most of the room is squared upwards normally and the caller is calling his normal choreography to them, at speed. A dancer led group squares up in a hexagon in the back of the hall and attempts to dance the same choreography every bit the front squares. Depending on the skill of the group and the choreography, this tin can exist quite a challenge.

Bi-gons — if hexagon dancing is adding ii extra couples to a normal square, bi-gon dancing is taking away two couples from a normal square. Yous are still dancing normal, symmetric 8-person MWSD, but with but 4 of yous! Motion around the flagpole heart is twice the normal speed and twice equally far. All this is documented by Sue Curtis here.

Justin's comments

Clark asks if there is some style to know when to change 180 degree turns into 120 degree turns. In general, how do you lot know where to get in Hex dancing, and if every call "works"?

What y'all would like to exist able to merits is the post-obit:

Every call in symmetric four-couple square dancing has a well-defined analogous call in Hexagon dancing.

I say that nosotros can equally to the lowest degree claim this:

Every motion (path, traffic pattern) of symmetric 4-couple dancing has a well-defined analogous motion in Hexagon dancing.

If you lot can say that all calls in square dancing accept a well-defined traffic pattern, then y'all can say that all calls take a well-defined fashion to dance them in Hexagons. Then, the question is: do any calls have undefined traffic patterns?

I seem to recall learning one or two calls with pull-bys that could exist either with the inside or outside manus. The rule was "don't hurt anybody." Cross and Plow, mayhap? Or annihilation and Cantankerous?

The ambivalence simply makes a difference of course if it happens in the center of the square, and gives people a selection every bit to which direction around the heart of the square they travel. So, doing an Ends Cross Cast Back in the east coast or west declension style doesn't matter.

The claim higher up (every 4-couple motion has a well-defined 6-couple motion) can be backed up solidly by giving the mapping from one motion to the other. This is done nearly naturally in polar coordinates. If a dancer in a iv-couple square moves from

(a0, r0, d0) to (a1, r1, d1)

where a0 and a1 are the polar angles around the centre of the square, r0 and r1 are the distances from the center of the square, and d0 and d1 are the dancer'southward starting and concluding facing directions, then the equivalent 6-couple dancer'southward movement would change by the following:

( (a1-a0)*2/3, r1-r0, (d1-d0)-(a1-a0)*1/3 )

In English language:

All rotations around the center signal are reduced to 2/3 their amount. This is the "under achieve" dominion that you discuss in your newspaper.
All distances from the center map straight.

As you rotate effectually the eye of the square, you lot adjust your facing direction by 1/3 the angle in the reverse management.

It is important to non accept the angles modernistic 360! If a1 > a0, this implies counter-clockwise movement, and a1 < a0 implies clockwise motion.

This is just a mathematical mapping, and doesn't address the fact that the square will breath, and tend to line upwards in a Y or triangle. This will map a 2x4 to curved waves (or columns), between a Y and a triangle. But these are all equivalent — the of import thing is that this mapping gives you an "platonic" spot to stand on and direction to face up, which provide for a well-defined Hexagon interpretation of whatsoever 4-couple motility.

You can also apply this mapping to construct a picture of the equivalent Hexagon germination for any four-couple germination. Start with a picture of the iv-couple formation, centered at the origin. Cut it in half, at any bending through the center. Take the resulting half picture, and squeeze it from a 180-degree bending about the origin to a 120-degree angle. Replicate this distorted prototype twice, once rotated at 120 degrees and once at -120 degrees.

Andy Latto's comments

If you lot have two unlike traffic patterns for a call, they will terminate in different places in hexagon dancing if they laissez passer on dissimilar sides of the eye of the set. More than precisely, describe a loop from the starting position to the catastrophe position along ane traffic blueprint, and then returning to the starting position along the reverse of the other traffic pattern. If the "winding number" of this loop around the center (the net number of times it winds effectually the center; you can summate this if you like by integrating dtheta, and dividing past 2pi) is zero, then the two paths will lead to the same identify. For example, if someone shortcutted Teacup concatenation by turning 1/four instead of 5/iv, they would end up in a different place in hexagon dancing, crashing with someone else if the other person did v/4. And then if you wanted to dance C4 hexagons, you have to settle a few controversial calls, and you lot're OK. The ones I tin think of are which hand you pull by with in the center on Brand Magic, Cross and Plough, Scatter Broadcast, Get Commencement Form, and Change-O. Some people also have odd traffic patterns for Bias Merchandise Broadcast; I think that if you get-go in right-hand waves, you make a right-hand star. People who dance Cantankerous Chuck-a-Luck by quarter in, slither and pass thru instead of quarter in and crosstrail through would be justly punished for their mistake, but unlike the examples above, I don't think the traffic pattern is controversial here; they're just wrong.

Instead of extending to 12 people, you can in theory also contract to 4 people. This is not two-couple dancing, but honestly dancing any normal 8-person material with 4 people.

[Editor'southward note: This thought has gained a following at Tech Squares to the indicate that certain people can dance many Plus sequences in real time. Sue Curtis has written a tutorial on learning and dancing in this manner: Introduction to Bi-gons]

One style to do this is to draw a line on the floor through the center of the set. All 4 people stay on one side of this line. Whenever the phone call takes yous over the line, you run across the square to the position of your diagonal opposite, and continue his part.

To eliminate the running around, depict the half plane that yous are dancing on on a sheet of rubber, and stretch it so that the two sides of the boundary line join each other. Mathematically, if the line is the x-axis, but double the value of theta.

Dancing this mode in do would exist possible, merely quite hard until you lot got used to information technology. Having a copy of your flooring distorted appropriately to dance on would brand information technology much easier.

To understand resolving, imagine that four-person dancing was normal, and 8-person dancing was a gimmick that someone came upward with, like hexagon dancing is now. 4-person sequences always cease with the heads together and sides together, of course. Simply when danced with 8 people, sometimes 1 human being is with 3 woman, sometimes 2 man is with 4 woman, and sometimes neither of these happen, but the couples are out of sequence. If you want to explain to a 4-dancer caller (who has never seen eight dancers in a foursquare, doesn't quite believe it works, and doesn't want to call back about it) how to write cloth that volition resolve for eight dancers, you merely tell him the following rule:

For each of the 4 dancers, on their path from "bow to your partner" to "right and left chiliad", keep track of how many times (internet) they circle the heart of the set up; if this number is odd for all dancers or even for all dancers, the sequence works for 8 dancers.

If the number is even for the head man and odd for the head woman, the heads won't get their partners. If information technology is even for the heads and odd for the sides, it works for everyone, only they will be out of sequence.

The same bargain works for hexagon dancing, but instead of looking at the parity of the winding number, you await at the winding number mod three. If these numbers match for the head homo and the head woman, the heads get their partners, and similarly for the sides. If the heads accept the same number, say 0, and the sides have the same number, then yous will all get your partner, but you volition be out of sequence if the sides number is ane or 2; that's why there 3 sequences, equally yous observe.

So if you desire to write sequences that resolve for both squares and hexes, y'all just need to brand the winding numbers all differ by a multiple of 6. Or if you unremarkably choreograph for 8 dancers, just brand sure the winding numbers all differ by a multiple of 3; the multiples of two already work past virtue of the fact that the sequence works for eight dancers.

(If you object that these winding numbers aren't integers, just add together something on to make them all integers: they will all take the same partial part, because the sequence resolves as a 4-dancer sequence, so the head homo and head adult female are together, meaning they have the same value of theta (mod 2pi). Alternatively, just add together "promenade whatever the right fraction is" to the end of the sequence, and this will brand all the winding numbers integers.)

All this works because no-i ever touches the center of the gear up, so square dancing is really done on the punctured airplane. Dancing with eight, 12, or 4N dancers is lifting the motion of the dancers to a roofing space. These are the only covering spaces of the punctured plane, so in that location'southward no way to extend this hack further. If but at that place was a second spot that no dancer ever touched, the key group would be much bigger, and so at that place would exist many more covering spaces, and many more foreign ways to trip the light fantastic toe.

Challenge Dancing Observations

Justin has been particularly interested in some of the unusual consequences of the hexagon formation on certain Challenge calls and concepts. Here are some of his observations (slightly modified and reported by Clark).

It takes 12 Interlocked Diamond Circulates to go back to where you started! Yous tin can't "Check your Interlocked Diamond" because at that place is no four-dancer diamond, just one knotty 12-dancer one. The same goes for Blocks (or whatsoever 4-dancer formation whose distortion includes the flagpole heart).

Consider iii head men in the center of the prepare in a Correct-Hand Mini-Moving ridge. Counter Rotate 3/2 will get them back to where they started. Stable Counter Rotate 3/2 will go them back to where they started, only they will be turned around fifty-fifty though they danced it stable! This is because the overriding "Hexagon" concept is more than powerful than Stable, and ane tin can think of the wall moving as you lot motion effectually the flagpole center. Dancing Stable Counter Rotate 3/2 is much similar driving a 3 point turn. Recollect about it.

Consider the heads in the heart of the set in a normal Right-Hand Two-Faced Line. Couples Twosome Trade three times will get anybody back to where they started, just the couples will exist half sashayed fifty-fifty though they danced it twosome! Again, the overriding "Hexagon" concept trumps Twosome.

These are not just special cases — they actually makes perfect sense once you realize that the "Hexagon" concept redefines words and phrases similar "north", "due south", and "same wall". Every time you make one revolution about the flagpole centre of the square, north and s are swapped, and and so are e and w. So, after a Stable Counter Rotate 3/2, you are nevertheless facing the same direction, information technology's just that that direction has moved to the other side of the room! Similarly, for Twosome Trade three times, if y'all started east of your partner, even though you lot finish on the same spots but half sashayed, y'all are still east of your partner. This is because east is now in the opposite direction.

Another concept with interesting Hexagon ramifications is One time Removed. Consider a 2x4. (Refer to the "Equivalent Formations" figure above.) Tin y'all color with a unlike colour the separate groups of people who work once removed from each other? (Try it!) If the dancers piece of work in their spots, then the answer is no. Equally with both Interlocked Diamonds and Blocks, dancing Once Removed Circulates repeatedly would take you to all 12 positions. But if the dancers remove the distortion (as they often practice), perform the phone call, and and then replace the distortion, clearly there are iii distinct groups of 4, and every dancer tin can only terminate on one of the 4 spots in their group.

This is an case of Andy's observation that if there are two different traffic patterns that take you on unlike sides of the flagpole eye, they will finish on different spots in Hexagon dancing. So, to successfully dance Once Removed in Hexagons, in that location must be a rule that says y'all never (or always) remove the distortion before doing the telephone call.

Revised: $Date: 2010/11/03 17:05:00 $

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