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3d 5 Level Hex-Prism variants

Introduction

Several hex variants have appeared on the Chess Variant Pages, many of them on a hexagonal board of side 6. The oldest, by Siegmund Wellisch, does not have a rules page on this site yet. Later ones around when I joined these pages include those of Wladyslaw Glinski and Dave McCooey, along with Fergus Duniho's Hex Shogi and Roberto Lavieri's Toccata. Additions of my own include 4 Linepiece Hex chess, AltOrth, Anglojewish Chess, Hexgi, Hex Horngi, Horn Rimmed Compact (HRC) variants , Liu Yang, and Plattraum. Finally I have added one based on a slightly simplified version of Haynie's hexagonal Chess, using the simple Wellisch-orientation Brokers that can capture only straight ahead rather than the original variant's stronger pieces and swapping round the Wazrs and Viceroys so that the latter are not both bound to the same binding, and one based on Hexenspiel for completeness' sake. Trebuqi is not suited to this treatment as the Trilby on the middle level would in practice be another Trebuchet for want of levels far enough away, and I exclude Courier-style hex variants for similar reasons. I have also excluded Chevron Ranks and Gyokugi as level-changing versions of its pieces have yet to be named.

It occurred to me that one generic way to extend hex variants to 3d is putting pieces that would be similarly blocked by the front rank - or protective of each other if not blocked - on each level. Plainly it would not do to just have several levels the same as all the pieces without an orthogonal move - or with only a forward one - would be confined to their own level. Then I saw that levels could be arranged in a sort of Rook-Bishop-Queen-Bishop-Rook pattern, echoing FIDE Chess along the extra dimension. Thus the top and bottom levels would have the pieces from the 2d variants - save for replacing any royally-restricted piece with its capturable counterpart. The next two in would have the corresponding pieces moving one level for each coprime step or leap of its move. The middle level would have the compounds of the two, but with the royal restriction restored to the relevant piece, echoing the position of King as well as Queen in FIDE Chess.

The same logic can be applied to pieces from other boards such as the 9x9 Compact Hex Chess and Hourglass Hex Chess boards, which would give sizes of 305 and 325 respectively. I see the dimensions specified in the index to this page, however, as as the mainstream of the idea.

Setup

Thanks to this range of images I can show a wide sample of array extracts. To save space I show just the White camp and its vicinity.

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Each camp of the Wellisch-derived variant is as follows:

top and bottom levels

even levels

middle level

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Each camp of the Glinski-derived variant is as follows:

top and bottom levels

even levels

middle level

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Each camp of the McCooey-derived variant is as follows:

top and bottom levels

even levels

middle level

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Each camp of the HRC Wellisch-derived variant is as follows:

top and bottom levels

even levels

middle level

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Each camp of the HRC Revergent-derived variant is as follows:

top and bottom levels

even levels

middle level

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Each camp of the HRC McCooey-derived variant is as follows:

top and bottom levels

even levels

middle level

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Each camp of the Liu Yang-derived variant is as follows:

top and bottom levels

even levels

middle level

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Each camp of the simplified-Haynie's-derived variant is as follows:

top and bottom levels

even levels

middle level

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Each camp of the Hexenspiel-derived variant is as follows:

top and bottom levels

even levels

middle level

Pieces

Gaps indicate pieces not depicted in the array extracts above for which I have yet to decide on an image. Unless otherwise stated, pieces starting on the top and bottom levels are the original 2d hex piece.

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Symmetric pieces are defined the same way on both Glinski-level and Wellisch-level orientations.

Pieces starting on the top and bottom levels that can move either within a level or up or down a column and are unbound:Pieces starting on the same columns but the even levels, all able to move only between levels and unbound but some switching between odd and even levels:Pieces starting on the same columns but the middle levels are the compounds of the original piece and the even-level one and are unbound:
The DUCHESS moves any distance through empty intermediate cells along any of the 8 orthogonals and 6 hex diagonals.The PONTIFF moves any distance through empty intermediate cells along any of the 12 standard, and 12 hybrid, diagonals.WORLDRIDER
The COHEN differs from the Queen in that it turns 60° at each intermediate cell, either left or right but never both within the same move. When moving up or down it can move only one step.The LANDLSEXTUPLET differs from the Pontiff in that it turns 41° between standard, or 51° between hybrid, diagolnals at each intermediate cell, either left or right but never both within the same move, and spiralling up or down..CHAFCOHEN
The VICEREINE moves any distance through empty intermediate cells along any of the 8 orthogonals, or one step along any of the 6 xz`1hex diagonals.The DRUID moves any distance through empty intermediate cells along any of the 12 standard, or one step along any of the 12 hybrid, diagonals.WORLDQUEEN
The BESIEGER moves any distance through empty intermediate cells along any of the 6 hex diagonals, or one step along any of the 8 orthogonals.The CONGRESSMAN moves any distance through empty intermediate cells along any of the 12 hybrid, or one step along any of the 12 standard, diagonals.WORLDTRICORN
The ROOK moves any distance through empty intermediate cells along any of the 8 orthogonals.The BISHOP moves any distance through empty intermediate cells along any of the 12 standard diagonals.QUEEN
The FINCH differs from the Rook in that it turns 60° at each intermediate cell, either left or right but never both within the same move. When moving up or down it can move only one step.The BOYSEXTUPLET differs from the Bishop in that it turns 41° at each intermediate cell, either left or right but never both within the same move, and spiralling up or down.CHAFFINCH
The CANNON differs from the Rook in that when capturing it must pass through exactly one occupied cell.The ARROW differs from the Bishop in that when capturing it must pass through exactly one occupied cell.TANK
The DUKE moves one step along any of the 8 orthogonals and 6 hex diagonals. It is the capturable version of the Grandduke which is the original piece.The LANDLORD moves one step along any of the 12 standard, and 12 hybrid, diagonals and is levelswitching.WORLDRULER
The WAZIR moves one step along any of the 8 orthogonals. It is the capturable version of the General which is the original piece.The FERZ moves one step along any of the 12 standard diagonals and is levelswitching.KING or PRINCE
The Worldruler and King must be kept out of Check. As Haynie's hex really does have a capturable Wazir, the corresponding middle-level piece in that is a Prince that moves like ther King but is capturable.
The SENNIGHT makes any root-7 leap within its level and is bound to all of that level.The HEFFALUMP makes any 1:root-7 leap and is unbound and levelswitching.SHERIFF
The UNICORN moves any distance through empty intermediate cells along any of the 6 hex diagonals, and is bound to a third of its level.The DICORN moves any distance through empty intermediate cells along any of the 12 hybrid diagonals, and is bound to a third of all levels.TRICORN
The RABBI differs from the Unicorn in that it turns 60° at each intermediate cell, either left or right but never both within the same move.The RUMBASEXTUPLET differs from the Dicorn in that it turns 51° at each intermediate cell, either left or right but never both within the same move, and spiralling up or down.CHAFRABBI
The SLING differs from the Unicorn in that when capturing it must pass through exactly one occupied cell.The SWORD differs from the Dicorn in that when capturing it must pass through exactly one occupied cell.SLINGLINE
The VICEROY moves one step along any of the 6 hex diagonals, and is bound to a third of its level.The RUMBABA moves one step along any of the 6 hex diagonals, and is bound to a third of all levels.BELLMAN
Pieces starting on the top and bottom levels that can move up and down only with certain kinds of move:Pieces starting on the same columns but the even levels, all able to move only between levels:Pieces starting on the same columns but the middle levels are the compounds of the original piece and the even-level one:
The WAITER moves as a Wazir except when capturing, which it does as a Viceroy.The COOK moves as a Ferz except when capturing, which it does as a Rumbaba.RESTAURATEUR
The CONTRAWAITER moves as a Viceroy except when capturing, which it does as a Wazir.The CONTRACOOK moves as a Dicorn except when capturing, which it does as a Ferz.CONTRARESTAURATEUR
The WAITRESS moves as a Rook except when capturing, which it does as a Unicorn.The CHEF moves as a Rumbaba except when capturing, which it does as a Dicorn.RESTAURATEUSE
The CONTRAWAITRESS moves as a Unicorn except when capturing, which it does as a Rook.The CONTRACHEF moves as a Dicorn except when capturing, which it does as a Bishop.CONTRARESTAURATEUSE
The SHAMMES moves as a Finch except when capturing, which it does as a Rabbi.The COOKSEXTUPLET moves as a Boysextuplet except when capturing, which it does as a Rumbasextuplet.CHAFSHAMMES
The CONTRASHAMMES moves as a Rabbi except when capturing, which it does as a Finch.The CONTRACOOKSEXTUPLET moves as a Rumbasextuplet except when capturing, which it does as a Boysextuplet.CHAFCONTRASHAMMES
2d Toccata pieces are qualified with the word Rook afterwards, pieces starting on even levels with Bishop, and pieces starting on the middle level with Queen.

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Part-symmetric and forward-only pieces are generally differently defined on the two orientations, or apply only on one.

Starting on the top and bottom levels and moving either within a level or up or down a column and are unbound is the SUPERBRASSGENERAL moves one step along any of the 8 orthogonals and 3 forward hex diagonals.

Starting on the same columns but the even levels and moving only between levels and unbound but switching between odd and even levels is the SUPERPEARLGENERAL moves one step along any of the 12 standard, and 6 forward hybrid, diagonals. Starting on the same columns but the middle levels is their compound the SUPERPRINCGENERAL.

Pieces starting on the top and bottom levels that can move only within a level and are bound to all or part of that level: move descriptions are shoewn in green if specific to Glinski-level boards and in red if specific to Wellisch-level ones.

Pieces starting on the top and bottom levels that can move only within a level:Pieces starting on the same columns but the even levels:Pieces starting on the same columns but the middle levels are the compounds of the original piece and the even-level one:
The AZUREGENERAL moves one step along any of the 6 hex diagonals and 1 straight forward orthogonal or 2 forward orthogonals.The RUBYGENERAL moves one step along any of the 12 hybrid, and 2 straight forward or 4 forward standard, diagonals.BELLMGENERAL
The WING moves any distance through empty intermediate cells, and the POINT one step, along the 1 straight forward orthogonal or 2 forward orthogonals.The MITRE moves any distance through empty intermediate cells, and the CROSS one step, along the 2 straight forward or 4 forward standard diagonals.PRINCESS, PRINCELING
The HORN moves any distance through empty intermediate cells, and the SALTIRE one step, along the 2 forward hex diagonals or 1 straight forward hex diagonal.The DILEMMA moves any distance through empty intermediate cells, and the RUMCHICK one step, along the 4 forward or 2 straight forward hybrid diagonalsTRILEMMA, BELLBOY
The SUPERSENHELM makes any of the 4 forwardmost Sennight leaps.The SUPERRUMTUSK makes any of the 8 forwardmost Heffalump leaps.SUPERRUSHOFF
The SENHELM makes either of the 2 forwardmost Sennight leaps.The RUMTUSK makes either of the 4 forwardmost Heffalump leaps.RUSHOFF
The BROKER moves as a Point except when capturing, which it does as a Saltire.The WIELDER moves as a Point except when capturing, which it does as a Saltire.BROKERWIELDER.

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Three Horn Rimmed pieces are specific to the Wellisch orientation.

Starting on the top and bottom levels is the SUPERSALTIRE moving one step along any of the 1 straight forward, and 2 half-forward, hex diagonals.
Starting on the even levels is the SUPERRUMCHICK moving one step along any of the 2 straight forward, and 4 half-forward, hybrid diagonals.
Starting on the middle level is their compound the SUPERBELLBOY.

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AltOrth pieces are specific to the Glinski orientation.

Pieces starting on the top and bottom levels that can move either within a level or - if not forward-only - up or down a column and are unbound:Pieces starting on the same columns but the even levels, all able to move only between levels and all but the Mitre and Dilemma switching between odd and even levels:Pieces starting on the same columns but the middle levels are the compounds of the original piece and the even-level one:
The FOREROOK moves any distance through empty intermediate cells along the 1 straight forward, 2 half-backward, and 2 interhex, orthogonals.The FOREBISHOP moves any distance through empty intermediate cells along the 2 straight forward, and 4 half-backward, standard diagonals.FOREQUEEN
The HINDROOK moves any distance through empty intermediate cells along the 2 half forward, 1 straight backward, and 2 interhex, orthogonals.The HINDBISHOP moves any distance through empty intermediate cells along the 4 half forward, and 2 straight backward, standard diagonals.HINDQUEEN
The FORECANNON and HINDCANNON differ from the Forerook and Hindrook in that when capturing they must pass through exactly one occupied cell.The FOREARROW and HINDARROW differ from the Forebishop and Hindbishop in that when capturing they must pass through exactly one occupied cell.FORETANK and HINDTANK
The BRIGADIER moves one step along any orthogonal except the straight backward one.The CROSSED BRIGADIER moves one step along any standard diagonal except the 2 straight backward ones.PRINCELY BRIGADIER
The COLONEL moves one step along any forward or interhex orthogonal or the straight backward one.The CROSSED COLONEL moves one step along any forward standard diagonal or the 2 straight backward ones.PRINCELY COLONEL
The WINGRESERVIST moves any distance through empty intermediate cells, and the POINTRESERVIST one step, along the 2 half-forward orthogonals.The MITRERESERVIST moves any distance through empty intermediate cells, and the CROSSRESERVIST one step, along the 2 half-forward orthogonals.PRINCRESERVIST.
Three divergent AltOrth pieces also appear in the Glinski-derived variant.
Starting on the top and bottom levels is the MIGRANT moving as a Point except when it captures, which it does as a Pointreservist.
Starting on the even levels is the MIGRANT CROSS moving as a Cross except when it captures, which it does as a Crossreservist.
Starting on the middle level is their compound the MIGRANT PRINCELING.

Rules

Unless otherwise stated rules are inherited from the 2d variant, but some clarifications are useful. If any further ones need adding I will gladly add them.

Pieces starting on the top and bottom levels are promotable to the same pieces as in 2d, and pieces starting on intermediate ranks are promotable to the corresponding pieces. For example, in 3d Hex Shogi a Rook is still promoted to a Vicereine, a Bishop to a Pontiff, and a Queen to a Worldqueen.

Thus works in reverse with pieces captured and reintroduced. Thus in 3d Horn Rimmed Hex a Rook returns as a Wing, a Bishop as a Mitre, and a Queen as a Princess.

Any double-step move applying to 2d still applies, and is extrapolated to other levels. Thus McCooey's optional double-step noncapturing initial move for Brokers also applies to Wielders and Brokerwielders.

Liu Yang's Grandduke swap becomes a Worldruler Swap in 3d, with no special powers for the capturable Duke and Landlord.

Notes

The combination of Cook with Waiter and Chef with Waitress to form Restaurateur and Restaurateuse reminds me of my joke about the man who tried to set up a restaurant as a one-man business. He was a chef first and a... (the pause is key to the pun) waiter second!



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By Charles Gilman.
Web page created: 2006-04-21. Web page last updated: 2016-06-14