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http://www.chessbase.com/puzzle/puzz03a.htm,
there Loyd's mate in 5 requires the unexpected Pawn to promote to Queen for the task. The Helpmate problem at issue now is whether from the starting array Black Pawn-a7 can deliver mate with no other piece assisting in 9 moves and without promotion -- of course as Helpmate White moves favourably towards the end result.
http://en.wikipedia.org/wiki/Excelsior_(chess_problem)

http://www.chessvariants.org/index/displaycomment.php?commentid=26784,
http://www.chessvariants.org/index/displaycomment.php?commentid=26783.
Six of th 30 result in: BQ 2 to mate;  WQ 3; B-f1 3; B-f8 3; N-g8 6 to
mate; N-g1 7 to mate. Now a new one, Rook-h8 can mate unassisted by a
fellow in 8 moves from the 500-year-old array RNBQKBNR as follows:
1 e4 d5
2 e4xd5            Qxd5
3 a3 (''waiting'') B c8-g4 
4 b3 (waiting)     B g4-f3
5 g2xf3            Q d5-d3
6 c2xd3            h5
7 K e1-e2          R h8-h6
8 h3 (waiting)     R h6-e6#. Checkmate by Rook alone from standard array.  We can easily generalize in follow-up table to the other Rooks.  How closely Queen-side Bishop and Knight work to the solved King-side cases is yet to determine, but within view. What about Pawns?  In perfect case this problem sub-genre, Pawn can/must be covered by any one piece, unlike when Piece is the candidate checker, but still Pawn must ''unassisted'' complete Mate. Can Pawn-a7 deliver mate unassisted and without promotion and how quickly? Is 10 moves still possible?
[http://www.chessvariants.org/index/displaycomment.php?commentid=26782.
ChessboardMath11 has nearly overflow 25 comments where Helpmates started with the three link-comments.]

Dear Mr. Duke:

You don't know how much pleased I am for your quoting in thoughts. In a
time that Ive been feeling unapreciated in my job, see a person half-world
away that I admire quoting me as 'brain food' gives me the strenght to
keep going.

Hugs

Super-Chimera and hyper-Chimera draw on these for their definitions: 
http://www.chessvariants.org/large.dir/contest84/ramayanachess.html,
http://www.chessvariants.org/diffmove.dir/hfantasy.html,
http://www.chessvariants.org/index/displaycomment.php?commentid=24314.

I could say the same thing if only A and T were to play: Displacement Chess 2 or Fischer Random. In the end, a chess variant will have to stand on its own by attracting new players and not depend on those who play the orthodox variety to switch to this new game.

Off the grid.  Make your piece-moves self-sustaining.  As it were,
bio-diverse: Camel, Zebra, Squirrel, Frog, Eagle, Bison, Hawk, Scorpion. 
Proliferation in its time.  Shove a pawn and the same pawn and that's a
crime. It is just illegal by Contingency Pawns' having their rights
revoked.  No right of first refusal, but in toto negation and denial. There is always some related cross-category contrarian CV milieu.  Here try Anti-King, Berolina, Losing Chess, Cylindrical, Closing Time for also
subverting a usual order in reversal outside the box. Penny for your any
thought a sure CV in the making, so write it down.  Or plain penny ante in
the sense of coins making good piece-markers on bill or napkin at the bar.
Contingency Pawn King must move once before his e-Pawn can begin.  It is
the same rule for all the pieces.  A typical opening series, 1 N-f3, 2
g2-g3, 3 B-g2, and White King indeed is able to move as early as fourth,
though Pawns but two remain immobile. '4 King e1-f1', vacated by the
Bishop thankfully for King safety, is one alternative.  Freed at last, '5
Pawn e2-e4', and the Queen stepping forward one subsequently helping
protect King some interim -- reasonable strategical logistic as ironically
more powerful Contingency Pawns always delay unavoidably in development. 
By now things return to normal with four Pawns already moveable or moved,
and this King has only forfeited castling for safety.  The second and more
common substitute preference is that Castling, as these three move, then '4
0-0' g-Pawn having advanced beforehand (so watch the Bishop lines),
getting used to new formations.

The Contingency Pawn actually expands opening possibilities.  There is a
world championship on right now,
http://www.chessbase.com/newsdetail.asp?newsid=6290. So far in four
games, what did they open with? game 1, Pawn-d4; game 2, Pawn-d4; game 3,
Pawn-d4; game 4, Pawn-d4. How many CVs would have such channeled same-old
opening obsession? Maybe none.  If Anand and Topalov were playing Great
Shatranj, they would not be duplicating openings from last decade and
century. If A. and T. were playing representative Schoolbook Chess for the
world championship instead of their particular entrenched-orthodoxy strong
Queen Shatranj that everybody knows and loves/hates, there would not be the
same first fifteen moves for the thousandth time. Specific Contingency Pawn
explained this thread on 8x8 can have openings N-a3, N-c3, N-f3, and N-h3.
Each one is different. All four would be used, and 'd4' or 'e4' would
really be illegal.  'd4' is illegal because Pawn cannot move until her
piece behind has.  Opening books become passe one way or another. 
Computers a while will waffle helplessly.  The best players may reside in
unknown hinterlands, not cosmopolitan Europe.  The lure of unknown futures
ripe with chance, fraught with challenge, not robotic control's electronic
feudalism under which we mostly live bent on absolute homogenization. 
Rhymie-stymie: 'Collect' proves correct moves connect grooves.

RNBQKBNR.  Middles Ages Knight's Leap perfectly matches the Contingency
Pawn since Knight has the only standard leap; if one attacks, King easily
takes Knight.  That would be either K x d3 or K x f3.  Then at once Pawn
e2-e4 becomes belated possibility, and King is unhurt within palace
protection potential by stepping to e3 or e2 behind the dilatory but
effective e-Pawn  -- 'e' for effective. So Contingency Pawn brings but
little baggage: Knight's Leap and the Rank Obligation. Player faces all
nine situations in stages progressive: all eight Pawns inert in starting
array; seven inert one activated; six two; five three; four four; three
five; two six; one seven; and all eight mobilizable. They are of course not at any time compelled to move or capture, but gain the capability upon each Piece behind her exiting.  In interims, one or several Pawns may be haplessly captured before moved or moveable. Thus capture and move ability are coterminus and inseparable, triggered by the Piece. One by one by one whilst so long as Piece has his matching Pawn fronting him, as Chess is played.  Piece moves once, then Pawn is free at last and once. The only inconvenience keeping track is infrequent return of Piece when Pawn remains free upon the pre-existing contingency. Pawns inert at first are counter-intuitive and chilling but necessary, and otherwise paired Pieces would openly face each other down such as crazy opening '1 R a1 x a8'.  No way. The initial passive Pawn rows are vital extravagance, employing neither drops nor so-called ''gating'' from outside, as best way later to enter the fray, present hidden force the Pawns herself. Pawns will achieve more respect as their strength grows -- referring now to the RANK OBLIGATION, which progresses Rank Two to Rank Three to Rank Four. Pawn naturally slides unimpeded to the final rank and promotion, when the way is thoroughly clear. For example, 'd4-d8
promotes to Queen' implies d5, d6 and d7 vacant, having neither sides
Pieces or Pawns in occupation. This promotion sometimes even occurs in the two minimal efficient 
steps only, like 'h2-h4' then 'h4-h8'.  More mutation, than promotion that would be. Or evolution as retribution. [Deservedly off-subject ill-effect analogy: as some ''evolved'' ''homo sapiens economicus stupidus'' or whoever now destroys in our very little lifetime species and ecologies along with the incidental weather, and it is rude taboo even mentioning the biggest events since the dinosaur extraterrestrial impact in quite some time.]

In sum, on 8x8 there can be no opening R-a1 x R-a8 because of the
intervening Pawn rows, despite Rooks' 1400-year unprotection in the array.
Is one or another a fallacy?  Now Contigency Pawns initially are inert, but
capturable, and serve the purpose to separate all the pieces paired across,
not just Rooks. Once Rook has moved, C. Pawn-a2 instantly acquires her full normal power, and the same for all Pieces having to precede their
corresponding C. Pawn.  In fact, C. Pawns become stronger than f.i.d.e.
orthodox Pawns on account of the accompanying RANK OBLIGATION. Most
observers have been familiar with rank-two two-step since youth.  Actually, if free and clear ahead, options two-step from rank 2, three-step rank 3, and four-step rank 4 all obtain, along with the regular divergent one-step.  ''Divergent'' because of the move and capture divergence, now taken for granted, unique for Pawn.  Contingency Pawn too captures always one step diagonal.  Now 'square-e4' is likeliest to become occupied by opposing Knight from g8 to f6 to e4, as White 'Pawn e2-e4' is impossible until King has moved sometime later, either castling or one-stepping.  More symmetry holds than usual, matching Piece and Pawn, and Pawns can no longer seem to be loose cannons trying utmost to lead development.  No more the sitting to Chess and just pushing Pawn, in hope for the best, or least bad outcome. Over the board, literally touching Cont. Pawn in error is light matter, if and when she cannot anyway move yet.  [Incidentally, when player touches Knight at say h8 with his own-side pieces situated nearby at f7 and g6, what persistent
obligation can there be? None whatsoever.]

All F.i.d.e. rules apply. Superficially, you might think, since Contingency Pawns are immobilized, Knight has a quick fool's mate.  Not so. If 1 N b1-c3 N g8-f6  2 N c3-b5, then 2 ... N f6-e4, and Black Knight is inviolate thwarting any checking move to d6, since White Pawns cannot move either, although himself, the Knight, off-centre for the same finale on the White King. If then the g1-Knight starts out, that gives Black time to move Pawn g7 and exit the Bishop.  If instead, contrary to move towards King, White moves 2 Pawn b2-b3, that Pawn can any move later advance three whilst
unimpeded b3-b6 by the RANK OBLIGATION.  Yet from b6 she has no evident
advantage to take a7 or c7 because she can be gobbled immediately by Rook
or Queen.  So it goes in normal development needing long-term planning not
subject to fast fixes and fusses.  Being possible Computer may find an
opening spoiler, baffler or outright cook, as designers, we just hereby now give King the mediaeval one-time King's leap Knight-like -- which should
be sufficient in the event -- as final add-on rule accompanying the
Contingency Pawn Mutator just in case. Moreover, King's Leap and obligatory Knight openings are aesthetic pair. 
Thus in the large, King may Castle
as usual, maneuvre with central Pawns to ''palace,'' or exercise
King's leap once only.  After a Castle, no King's leap allowed, but the
singular Leap and routine palacing are very mutually compatible.  Little 8x8 is not
the main feature for Contingency Pawns, rather 8x10 and 10x10, which are
having ancient 13-century Gryphon and new-fangled Bison (who is liberally
applied unnuanced Falcon, invented 1992).

When Pawns are Contingency in antique standard 8x8, RNBQKBNR, there are
four openings: N-a3, N-c3, N-f3, N-h3.  Once Knight is out, Knight Cont.
Pawn can move b2-b3 or b2-b4.  In the normal game, from b3 she has
immediate three-step option to b6, from which she can capture to a7 or c7,
the black Pawn row.  So Black needs to hurry up development of
Black-b-Knight and/or b-Pawn. The four-step option from rank-four, and
promotion that way rank-8, is unlikely to avail before late mid-game even as
a threat. Once the Knight Cont. Pawn is moved, Bishop has an easy way
out, and Rook or Queen can slide over to where Knight and Bishop began, so
it is pretty regular development by then.  Pieces generally have formation
ahead of lagging Pawn phalanxes. Contingency Pawn speeds development on any size board, smallish 8x8 here as well.  Mastery of principles of cadence enables Pawns to keep pace behind the Pieces. To protect King, there are normal castling and also free use of d2-d3 and e2-e3 to form centrally a safety palace for the King to situate, ''palacing'' in jargon. Contingency Pawns work far better than diagonal Berolina.  They prohibit generalized three-stepping by typical Pawns for 10-deep boards.  '10x10' then also includes five-stepping option from rank 5 with immediate promotion, to go with two 2, three rank 3, and four rank 4.  Thus ''opening two-step'' from rank 2 amplifies logically to all the conceivable others.  With these indicated full ''rank options,'' the alternative step always matching the present rank of the Pawn as a matter of course, the perfect ratio of power Pawns/Pieces is maintained more or less exactly as to have its delta indeterminant from CV to CV. One of the constants of nature within everlasting diversity in professional CV design.

The Contingency Pawn cannot move until her piece has once. Cont. Pawn
cannot even capture before of course by the rule, necessitating a look at Rank 3/8.  The 8x10 array is
Bison-Gryphon-Bishop-Knight-Amazon-King-Knight-Bishop-Gryphon-Bison,
covering all Pawns thrice, twice, or once at least. The Cont.-Pawn Mutator
exponentially speeds development in having each piece come forth first and
his Pawn sometime second. There are no real immediate mate threats or
likely fool's mate because of adequate counterplay by familiar leapers Bison,
(partially) Amazon, and Knight. It is peculiar that Bison, Gryphon, and
Bishop are unprotected in the starting array, like Rook is not in RNBQKBNR;
but it does not present a problem, because Knight's first move opens
Amazon to guard Bishop.  Next, most rank-three squares are protected even without
Pawn's one-step diagonal (capture) by those leading leaping back-rankers.
Only a3, b3, i3, j3 need rationalization as unguarded. Well, once Bison leaps, Pawn-a2 inevitably immediately covers b3-kindreds by the very mutating-rule itself, like Scylla and Charybdis or like proverbial Horse and Carriage. That is ex post protection enough, being in just one move only. And it leaves only a3-counterparts still to consider explaining away. 'a3' is far off to be worrisome to King. So this question is just matter of cheap exchanges. Now opposite Bisons cannot reach the (empty) a3, or a6 or j3 or j6, in two moves. Perfect. Nor can Knights. Only Amazon can. So, if 'Amazon 1 ...e8-d6' threatens vacant but somehow awkward a3, with all the ramifications, if any, of occupation of same, requiring to be sure in the real world hypothetical follow-up same-side supporting cast anon for full effect -- simply '2 Bison j1-g3(!)' from the opposite corner! Then if Amazon were dare to try the empty post by  'X ...d6-a3', '[X+1] Bison g3-d5'  would fork King and Amazon, potentially only on the third, or even second move if White were the one starting off provocatively that way instead! In fact, those earliest possible cases would actually be the obligatory fool's mates to find too. So that in overview, no, there do not appear to be any highly or even moderately deficient spaces, not even one, among the 30 squares a1-j1, a2-j2, a3-j3. Cont. Pawns as one Way/Wave/Grave of the future, are any two CVs alike? 
Thankfully, like snowflakes, of course not. Any one CV of CVPage 1000 CVs could and should warrant its own library of 10000 volumes in analysis one per designee.

700-year-old hook-moving Gryphon protects Bison Pawns a and j in
Bn-G-Bp-N-Amazon-K-N-Bp-G-Bn. All other pawns are twice array-protected and thrice by the King. So required ''piece-developed-first'' does not play havoc with early pawn attacks. They just are no more feasible than usual. If 1 Bison a1-b4, 1 ...N-c6 quickly doubly protects Black Pawn-a7; and so on.  In Contingency Pawn CVs, pieces must draw out the Pawns, preceding them.  No 'e2-e4' until Amazon behind has moved away!  Central King Pawn-f2 is array-stuck until King himself castles or is forced from his beginning f1. Recognizable mid-games are nil, because here pieces fronting the Pawns tend to form outer shield, an advance perimetre, for the Pawns within. Mid-games involve some back-protecting of forward pieces who will want to return behind relative safety of Pawn phalanxes. Contingency Pawn games may benefit from other optional contingency.  One, sides may agree in advance a subvariant each Pawn has additional non-capturing forward-advance option
according to number of her present rank position.  It perfectly fits the
initial-array rank-two optional two-step: 2 and 2.  Then rank three a
three-step (3 and 3) to rank 6, and rank four to eight (4 and 4) and
instant promotion.  Reverses for Black.  Usually those three-steppings and
four-steppings with the board but eight-deep are solidly blocked.  Since
the year 1500, Pawn initial two-step has always had this IMPLICIT rare
three-step and four-step from ranks 3 and 4 respectively by plain sheer
logic, insofar as the pro-active ability hinges on her rank. You just do not see it a lot. In future,
when sitting for Chess, ''do you play two-step?'' means also
three/rank-3 and four/rank-4 as inclusive package-mutator for variegated
Cont. Pawns. The spice of life.

The Contingency Pawn is stuck until her counterpart-piece behind moves
away. Pieces move, then Pawns. Since 13th-century Gryphon may stop at one
diagonal before the 45-degree orthogonal continuation, all Pawns are
protected in: Bison-Gryphon-Bishop-Knight-Amazon-King-N-Bp-G-Bn. Board is
8x10. If expecting opening like d2-d4 or e2-e4, think again. Knight must
move first d1-c3, and then anytime later d2-d4 or d2-d3 is permissible for
that Contingency Pawn. Likewise Amazon moves out e1-f3, enabling Cont. Pawn
in e-file to follow soon with e2-e4. The whole back rank potentially opens
up that way, but piece in Rank 1 must always precede his Cont. Pawn Rank 2
of same file. Net result is no dilly-dally opening development as pieces exit first.
If Chessist Lewis Carroll invented her, he might write, mixing it up like
the movies: ''Mome Gryphon, Slithy Jabberwock/ In frumious opening
hammerlock/ 'Twas brillig of the vorpal score/ Gyre, gimble to e-4 no
more./ Mock mimsy pieces' beamish way/ Contingent Pawns uffish delay.'' 
http://www.jabberwocky.com/carroll/jabber/jabberwocky.html

CV designers might learn to advance Caissa's future not their own
well-deserved artistry for art's sake. Turn the beat around, starting with
Pawns. Literally, start with Pawns as born before pieces. First, come up
with a really good Pawn-type on your own.  Only then, after Pawn is
polished and perfected, REVERSE ENGINEER appropriate rules and pieces for
best effect. On average, they, Pawns, are half the forces, are they not? 
The better half.  So why are Pawns dealt with in last-paragraph patchwork
of rules-sets?  Designers are treating their pawns like afterthoughts when
they need front placing as order of the day. Here is example of brand-new
Pawn-type class, the Contingency Pawn, in specific algorithmic development. (Step One) The inventive step(!): Pawn only moves after her orthogonal piece behind has left the array position! This step may be facilitated but never controlled, being unfathomable. (Step Two) Since Step One happens to be radical enough here, contingency Pawn's move should be regular standard F.i.d.e. 8x10 and standard Eurasian with North capture too 10x10. Inseparable initial two-step and En Passant apply both cases, like Railroad engine and caboose. (Step Three) Cold calculation. What piece-types can leave array before pawns have moved? It should spring to mind. Leapers and leapers, j.c. It is not necessary to have all leapers, though, because once several leap, lots of adjacent lines open for diagonal- and hook-movers. Leapers should predominate, or reach 1/2, so openings are not too channelled. Result, initial array:
Bison-Gryphon-Bishop-Knight-Amazon-King-Knight-Bishop-Gryphon-Bison. (Step
Five) Polish the details of this CONTINGENCY PAWN. Stipulate free castling
with either array-corner Bison. Eliminate all other ambiguities. (Step Six) Realize this is a PAWN-CLASS and many other Contigencies are possible, arguable infinite but probably not, so do not tiresomely claim one CV only, but thousands, and more. //// Following these slashes are other CVs, Contingency Pawns-like, after all the above is called Mode A; Modes B, C, D.... //// alternative Mode B> Pawn moves only if following an ''event,'' defined as a check or a capture; [To this exact very day, six(6) years ago, I defined an event, which should be everybody's basic CV vocabulary, as
http://www.chessvariants.org/index/displaycomment.php?commentid=5482.]
 C> Pawn contingency enables extra option of non-capturing move up to number of her rank or her file; D> Cont. Pawn, as f.i.d.e. or Eurasian, only moves on odd-numbered turns; E> Cont. Pawn only moves if adjacent to three+ same-side units, which holds in array of course, to the tune of five, or four, adjacent, more than enough.

64-   .            Artificially, Squares have that extra
 cell  ._.           unnecessary side, making four.  Sans
board ._._.  2-4     rank and sans file, Triangles have Cell
     ._._._. III     and Level, redundantly for convenience.
    ._._._._. IV     Corner Bishop triangles are 1,2,4,5,7,9,10...
   ._._._._._. V     With one compulsory horizontal side, there are
  ._._._._._._.      only two orientations and so two types of cells,
 ._._._._._._._.     up and down.  Corner Bishop's are /_\ and
._._._._._._._._.    Interior Bishop's the opposite, down, at a 
(Level VIII 50-64)   glance. For annotative intricacy, if (Cell + Level) is even, it is corner Bishop cell. Such as 'Level VII Cell 48' is odd and
belongs to interior Bishop. Interior Bishop reaches 28 and corner Bishop
36. That fits in that the board is 8^8^8 and 36-8 = 28. How about a
colourbound Knight on these primitive superior equiangular triangles? 
Rather than two Knight-types, additionally allow Knight diagonal through
vertex one-step at option -- making one pure Knight piece-type and eliminating
the prospect of detracting colourboundedness.  The only other uses of that
Knight-vertex-diagonal one-step are King himself and Pawn capture-mode, since Bishop (and Queen) has different actuation. Then Knight, like Rook, reaches all the cells and becomes of somewhat more value than either Bishop in triangles.  R > N > corner B > interior B. That the omni-Pawn has higher value than interior Bishop is yet unconfirmed, but they are pretty close. The better CV here appears to dispense with one Rook, as KQRBBNNPPPPPP. Six Pawns and
one Rook.  Promotion to R,N,B at opposite side excluding the Cell 1 Level
I. Kings start at 50 and 64. Array-placement mobilization is by order:
Black put 1/2 pieces, White 1/2, Black 1/2, White 1/2, White Pawns, Black
Pawns. White moves first. All else strict standard F.I.D.E. -- sans squares.

64 cells  .          F.i.d.e.'s going to triangles, troika, would
         ._.         mean brand new, fresh start opening 
 II     ._._. 234    theory with retention of holy of holies 
III    ._._._. 5-9   sixty-four. Study triangles for a twenty-
 IV   ._._._._.      four period and squares are unnatural. In
  V  ._._._._._.     both square and triangle, unlike hexagon,
 VI ._._._._._._.    Rook cannot triangulate. Rook circumnavigating
   ._._._._._._._.   the board goes 50-3-64-51 ending over one cell
  ._._._._._._._._.  from origination whilst not entering #1 --
 (Level VIII 50-64)  contrasted to squares' 4-move circumnavigation. Rook
mandatorily switches Bishop binding precisely from turn to turn, like Knight does in
squares.  Knight's two-step through side or vertex is colourbound, enabling two types, corner and interior, as with Bishops; alternatively let the two Knights have the Pawn-capturing one-step through vertex at option for neater colourswitching availability in one pure Equine piece-type. On standard 64 the corner Bishop reaches
36 spaces and the interior Bishop 28 spaces for necessary magnified value differential
at about 3.5 to 2.5. Strong omni-Pawns work best, one-stepping through
side to move and vertex to capture. Promotion should exclude Queen.  The opening imperative for the first ten moves is tug between Castling King from array 50 and 64 on one hand and control of valuable real estate, the center, triangles 21, 30, 31, 32. Whoso controls those four will have the presumptive edge, other things being equal. Ironically, King Castling to 26 is counterintuitively rather towards that center, but he does not wish to step any closer. Scads of equilateral triangular boards are possible from about 4^4^4 to about 16^16^16 each with its untold THOUSANDS of VARIANTS of core classical Chess on the triadic theme. Use your imagination: two-move, AMAZON, Fischer arrays, NIGHTRIDER, cylindrical, royal Knight, you name it.

. Triangular / King cornered to start is interesting because
  I     ._.  F.i.d.e. / there is only one step out from triangle 50.
 II    ._._.  board   / King has that Rook one-step 50-51.  With board
5-9   ._._._.  of 64  / equilateral triangular in the large, K 50-26
 IV  ._._._._.  cells / is actually a Bishop two-step over cell 37, 
  V ._._._._._.         not a Rook. That is the better logic of using
 VI._._._._._._.        triangles.  Now from more central 26 King is 
  ._._._._._._._.       safer. Three choices to move exist from there,
 ._._._._._._._._.      26-27, 26-38 and 26-40.  More likely he will be 
(Level VIII 50-64)      surrounded by Pawns and pieces there protecting one another mutually.  So, Triangle 26 is ideal standard Castling location, and White's corresponding is 36 for considerable separation. Rook's going to 37, Bunko Leap, in the Castling puts Rook a single step from 51, which is a co-intersection with 50 of the longest Rook ''files.''  For example, Rook 51-64 is 7 steps notionally across 13 equilateral triangles. Thus fixed Castling, Rook towards the corner and King towards the center, helps both of them. King can safely exit his dangerous lock-in at corner with only the one escape by timely Castle. The admonition to Castle Early transposes from F.id.e. squares to triangles in unchanged 64.
For visualization: http://www.chessvariants.org/shape.dir/klinzha/klinzha.html.
http://www.chessvariants.org/index/displaycomment.php?commentid=25177

http://www.chessvariants.org/index/listcomments.php?subjectid=ChessboardMath10
has Tetraktys and more triangles.
         .        Flowerman inquired about small Chess, and now we
 I      ._.       have a wholly new geometry. Triangles, out of
II     ._._.      ancient Tetraktys, nine-celled. F.i.d.e.-64 works
5-9   ._._._.     fine in equilateral triangles. All F.I.D.E. rules
IV   ._._._._.    apply respecting stalemate, touch move, 50-move,
 V  ._._._._._.   etc. Opposing Kings start at two corners 50 and 64.
VI ._._._._._._.  Castling is two squares towards the safer center.
  ._._._._._._._. Black King goes to cell 26, and whereever Rook 
 ._._._._._._._._.is arrayed, Rook then goes to 37 if not already 
(Level VIII, 50-64) there. Either 'King 50-37' or just '0-0' is Castle,
and can be said ''King Castles'' and then ''Rook BUNKO LEAPs.''
King towards corner is called Bunker Leap in CVs, but here it's well Bunko
Leap for Rook instead (likely) going towards corner. They must not have
already moved, nor King be or move through check. Otherwise, F.i.d.e. Royal King one-steps through any side or vertex along a Knight half-path. Realize again Knight is straight as an arrow in triangles, either Dabbabah-like or Alfil-like: 
http://www.chessvariants.org/index/displaycomment.php?commentid=25236.
Finally, six Pawns, complementing the eight lined RRNNBBQK, one-step omnidirectionally, like CENTENNIAL Chess (#13 Next Chess), with same divergence of side without and vertex with capture. No promotion at common cell 1, Black promotes at 4,9,16,25,36,49,64, and White's promotion cells are all opposite. A Chess VARIANT of Triangular F.i.d.e. follows. If principle of mobilization is agreed on, it should go in order as: Black places 1/2 pieces, then White 1/2, Black 1/2, White 1/2, White Pawns, Black Pawns. No Pawns above Level IV, and no pieces within the interior triangle 54-21-60. Besides ChessboardMath10 above, -11 has triangles: http://www.chessvariants.org/index/listcomments.php?subjectid=ChessboardMath11.