Acronym | ex, pT | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Name |
hexacosachoron, 600-cell, hydrochoron, tetraplex, polytetrahedron | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Cross sections |
© or within some subsymmetries: © | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Circumradius | (1+sqrt(5))/2 = 1.618034 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Edge radius | sqrt[5+2 sqrt(5)]/2 = 1.538842 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Face radius | sqrt[(7+3 sqrt(5))/6] = 1.511523 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius | sqrt[(9+4 sqrt(5))/8] = 1.497676 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Density | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Vertex figure |
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Vertex layers |
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Lace city in approx. ASCII-art |
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Coordinates |
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General of army | (is itself convex) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polychoral members:
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Dual | hi | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Dihedral angles | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 120, 720, 1200, 600 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
As abstract polytope ex is isomorphic to gax, thereby replacing pentagonal edge figures by pentagrammal ones resp. replacing ike vertex figures by gike ones.
The tets of ex can be divided into 20 rings of 30 each. These stackings of tets, when non-bended into 4D (as shown to the right), then are what elsewhere is known as Boerdijk-Coxeter helix.
Diminishing ex at the vertex positions of an inscribed f-ico results in sadi. – Diminishing likewise at the vertex positions of 2 inscribed f-icoes, which mutually are not vertex incident, results in bidex. – Double-diminishing ex at the vertex positions of an inscribed f/q-hex, i.e. chopping off (intersecting) bistratic caps, results in f-tes. – Diminishing likewise at the vertex positions of an inscribed f-spid results in idimex.
The vertex figure of ex is the ike. Diminishing one vertex, the antipodal pair of vertices described by an there centered ike, the opposite of the ikes placed there, etc. outlines a full ring of 10 omitted vertices. Then there is an unique orthogonal similar ring. The thus diminishing then is nothing but gap. – Diminishing instead at alternate vertices of these 2 rings would result in bicypdex, the bi-cyclopentadiminishing of ex.
The description of ex as xffoo3oxoof3fooxo3ooffx&#zx (cf. below) shows that (as its 3rd layer) an f-spid could be vertex inscribed. In fact, the 60 spid compound 10{3,3,5}[60{;3,3,3;}] (dopix) has a (v-scaled) ex as its hull and reuses every vertex 10 times.
The number of ways to color the hexacosachoron with different colors per cell is 600!/7200 = 1.757739 · 101404. – This is because the color group is the permutation group of 600 elements and has size 600!, while the order of the pure rotational hecatonicosachoral group is 7 200. (The reflectional hecatonicosachoral group would have twice as many, i.e. 14 400 elements.)
Incidence matrix according to Dynkin symbol
x3o3o5o . . . . | 120 ♦ 12 | 30 | 20 --------+-----+-----+------+---- x . . . | 2 | 720 | 5 | 5 --------+-----+-----+------+---- x3o . . | 3 | 3 | 1200 | 2 --------+-----+-----+------+---- x3o3o . ♦ 4 | 6 | 4 | 600 snubbed forms: β3o3o5o
x3o3o5/4o . . . . | 120 ♦ 12 | 30 | 20 ----------+-----+-----+------+---- x . . . | 2 | 720 | 5 | 5 ----------+-----+-----+------+---- x3o . . | 3 | 3 | 1200 | 2 ----------+-----+-----+------+---- x3o3o . ♦ 4 | 6 | 4 | 600
x3o3/2o5o . . . . | 120 ♦ 12 | 30 | 20 ----------+-----+-----+------+---- x . . . | 2 | 720 | 5 | 5 ----------+-----+-----+------+---- x3o . . | 3 | 3 | 1200 | 2 ----------+-----+-----+------+---- x3o3/2o . ♦ 4 | 6 | 4 | 600
x3o3/2o5/4o . . . . | 120 ♦ 12 | 30 | 20 ------------+-----+-----+------+---- x . . . | 2 | 720 | 5 | 5 ------------+-----+-----+------+---- x3o . . | 3 | 3 | 1200 | 2 ------------+-----+-----+------+---- x3o3/2o . ♦ 4 | 6 | 4 | 600
x3/2o3o5o . . . . | 120 ♦ 12 | 30 | 20 ----------+-----+-----+------+---- x . . . | 2 | 720 | 5 | 5 ----------+-----+-----+------+---- x3/2o . . | 3 | 3 | 1200 | 2 ----------+-----+-----+------+---- x3/2o3o . ♦ 4 | 6 | 4 | 600
x3/2o3o5/4o . . . . | 120 ♦ 12 | 30 | 20 ------------+-----+-----+------+---- x . . . | 2 | 720 | 5 | 5 ------------+-----+-----+------+---- x3/2o . . | 3 | 3 | 1200 | 2 ------------+-----+-----+------+---- x3/2o3o . ♦ 4 | 6 | 4 | 600
x3/2o3/2o5o . . . . | 120 ♦ 12 | 30 | 20 ------------+-----+-----+------+---- x . . . | 2 | 720 | 5 | 5 ------------+-----+-----+------+---- x3/2o . . | 3 | 3 | 1200 | 2 ------------+-----+-----+------+---- x3/2o3/2o . ♦ 4 | 6 | 4 | 600
x3/2o3/2o5/4o . . . . | 120 ♦ 12 | 30 | 20 --------------+-----+-----+------+---- x . . . | 2 | 720 | 5 | 5 --------------+-----+-----+------+---- x3/2o . . | 3 | 3 | 1200 | 2 --------------+-----+-----+------+---- x3/2o3/2o . ♦ 4 | 6 | 4 | 600
oxofofoxo3ooooxoooo5ooxoooxoo&#xt → height(1,2) = height(3,4) = height(6,7) = height(8,9) = (sqrt(5)-1)/4 = 0.309017 height(2,3) = height(4,5) = height(5,6) = height(7,8) = 1/2 (pt || pseudo ike || pseudo doe || pseudo f-ike || pseudo id || pseudo f-ike || pseudo doe || pseudo ike || pt) o........3o........5o........ & | 2 * * * * ♦ 12 0 0 0 0 0 0 0 0 0 | 30 0 0 0 0 0 0 0 0 0 0 0 | 20 0 0 0 0 0 0 0 .o.......3.o.......5.o....... & | * 24 * * * ♦ 1 5 5 1 0 0 0 0 0 0 | 5 5 10 5 5 0 0 0 0 0 0 0 | 5 5 5 5 0 0 0 0 ..o......3..o......5..o...... & | * * 40 * * ♦ 0 0 3 0 3 3 3 0 0 0 | 0 0 3 6 3 6 3 3 6 0 0 0 | 0 1 3 6 1 3 6 0 ...o.....3...o.....5...o..... & | * * * 24 * ♦ 0 0 0 1 0 5 0 1 5 0 | 0 0 0 0 5 5 0 0 10 5 5 0 | 0 0 0 5 0 5 5 5 ....o....3....o....5....o.... | * * * * 30 ♦ 0 0 0 0 0 0 4 0 4 4 | 0 0 0 0 0 0 8 2 8 8 2 2 | 0 0 0 0 4 8 4 4 -------------------------------------+---------------+-----------------------------------+--------------------------------------------+--------------------------- oo.......3oo.......5oo.......&#x & | 1 1 0 0 0 | 24 * * * * * * * * * | 5 0 0 0 0 0 0 0 0 0 0 0 | 5 0 0 0 0 0 0 0 .x....... ......... ......... & | 0 2 0 0 0 | * 60 * * * * * * * * | 1 2 2 0 0 0 0 0 0 0 0 0 | 2 2 1 0 0 0 0 0 .oo......3.oo......5.oo......&#x & | 0 1 1 0 0 | * * 120 * * * * * * * | 0 0 2 2 1 0 0 0 0 0 0 0 | 0 1 2 2 0 0 0 0 .o.o.....3.o.o.....5.o.o.....&#x & | 0 1 0 1 0 | * * * 24 * * * * * * | 0 0 0 0 5 0 0 0 0 0 0 0 | 0 0 0 5 0 0 0 0 ......... ......... ..x...... & | 0 0 2 0 0 | * * * * 60 * * * * * | 0 0 0 2 0 2 0 1 0 0 0 0 | 0 0 1 2 0 0 2 0 ..oo.....3..oo.....5..oo.....&#x & | 0 0 1 1 0 | * * * * * 120 * * * * | 0 0 0 0 1 2 0 0 2 0 0 0 | 0 0 0 2 0 1 2 0 ..o.o....3..o.o....5..o.o....&#x & | 0 0 1 0 1 | * * * * * * 120 * * * | 0 0 0 0 0 0 2 1 2 0 0 0 | 0 0 0 0 1 2 2 0 ...o.o...3...o.o...5...o.o...&#x | 0 0 0 2 0 | * * * * * * * 12 * * | 0 0 0 0 0 0 0 0 0 0 5 0 | 0 0 0 0 0 0 0 5 ...oo....3...oo....5...oo....&#x & | 0 0 0 1 1 | * * * * * * * * 120 * | 0 0 0 0 0 0 0 0 2 2 1 0 | 0 0 0 0 0 2 1 2 ......... ....x.... ......... | 0 0 0 0 2 | * * * * * * * * * 60 | 0 0 0 0 0 0 2 0 0 2 0 1 | 0 0 0 0 2 2 0 1 -------------------------------------+---------------+-----------------------------------+--------------------------------------------+--------------------------- ox....... ......... .........&#x & | 1 2 0 0 0 | 2 1 0 0 0 0 0 0 0 0 | 60 * * * * * * * * * * * | 2 0 0 0 0 0 0 0 .x.......3.o....... ......... & | 0 3 0 0 0 | 0 3 0 0 0 0 0 0 0 0 | * 40 * * * * * * * * * * | 1 1 0 0 0 0 0 0 .xo...... ......... .........&#x & | 0 2 1 0 0 | 0 1 2 0 0 0 0 0 0 0 | * * 120 * * * * * * * * * | 0 1 1 0 0 0 0 0 ......... ......... .ox......&#x & | 0 1 2 0 0 | 0 0 2 0 1 0 0 0 0 0 | * * * 120 * * * * * * * * | 0 0 1 1 0 0 0 0 .ooo.....3.ooo.....5.ooo.....&#x & | 0 1 1 1 0 | 0 0 1 1 0 1 0 0 0 0 | * * * * 120 * * * * * * * | 0 0 0 2 0 0 0 0 ......... ......... ..xo.....&#x & | 0 0 2 1 0 | 0 0 0 0 1 2 0 0 0 0 | * * * * * 120 * * * * * * | 0 0 0 1 0 0 1 0 ......... ..o.x.... .........&#x & | 0 0 1 0 2 | 0 0 0 0 0 0 2 0 0 1 | * * * * * * 120 * * * * * | 0 0 0 0 1 1 0 0 ......... ......... ..x.o....&#x & | 0 0 2 0 1 | 0 0 0 0 1 0 2 0 0 0 | * * * * * * * 60 * * * * | 0 0 0 0 0 0 2 0 ..ooo....3..ooo....5..ooo....&#x & | 0 0 1 1 1 | 0 0 0 0 0 1 1 0 1 0 | * * * * * * * * 240 * * * | 0 0 0 0 0 1 1 0 ......... ...ox.... .........&#x & | 0 0 0 1 2 | 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * 120 * * | 0 0 0 0 0 1 0 1 ...ooo...3...ooo...5...ooo...&#x | 0 0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * 60 * | 0 0 0 0 0 0 0 2 ....o....3....x.... ......... | 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * 20 | 0 0 0 0 2 0 0 0 -------------------------------------+---------------+-----------------------------------+--------------------------------------------+--------------------------- ox.......3oo....... .........&#x & ♦ 1 3 0 0 0 | 3 3 0 0 0 0 0 0 0 0 | 3 1 0 0 0 0 0 0 0 0 0 0 | 40 * * * * * * * .xo......3.oo...... .........&#x & ♦ 0 3 1 0 0 | 0 3 3 0 0 0 0 0 0 0 | 0 1 3 0 0 0 0 0 0 0 0 0 | * 40 * * * * * * .xo...... ......... .ox......&#x & ♦ 0 2 2 0 0 | 0 1 4 0 1 0 0 0 0 0 | 0 0 2 2 0 0 0 0 0 0 0 0 | * * 60 * * * * * ......... ......... .oxo.....&#xt & ♦ 0 1 2 1 0 | 0 0 2 1 1 2 0 0 0 0 | 0 0 0 1 2 1 0 0 0 0 0 0 | * * * 120 * * * * ..o.o....3..o.x.... .........&#x & ♦ 0 0 1 0 3 | 0 0 0 0 0 0 3 0 0 3 | 0 0 0 0 0 0 3 0 0 0 0 1 | * * * * 40 * * * ......... ..oox.... .........&#xt & ♦ 0 0 1 1 2 | 0 0 0 0 0 1 2 0 2 1 | 0 0 0 0 0 0 1 0 2 1 0 0 | * * * * * 120 * * ......... ......... ..xoo....&#xt & ♦ 0 0 2 1 1 | 0 0 0 0 1 2 2 0 1 0 | 0 0 0 0 0 1 0 1 2 0 0 0 | * * * * * * 120 * ......... ...oxo... .........&#xt ♦ 0 0 0 2 2 | 0 0 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * 60
xoofoxFfoofxofo3oofoxfooofxofoo3ofoxfoofFxofoox&#xt → height(1,2) = height(3,4) = height(5,6) = height(7,8) = height(8,9) = height(10,11) = height(12,13) = height(14,15) = sqrt[3-sqrt(5)]/4 = 0.218508 height(2,3) = height(6,7) = height(9,10) = height(13,14) = sqrt[7-3 sqrt(5)]/4 = 0.135045 height(4,5) = height(11,12) = 1/sqrt(8) = 0.353553 (tet || pseudo inv f-tet || pseudo f-oct || pseudo (f,x)-co || pseudo inv (f,x)-tut || pseudo (x,f)-tut || pseudo F-tet || pseudo f-co || pseudo inv F-tet || pseudo inv (x,f)-tut || || pseudo (f,x)-tut || pseudo (x,f)-co || pseudo f-oct || pseudo f-tet || inv tet) o..............3o..............3o.............. & | 8 * * * * * * * ♦ 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 6 3 3 6 3 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 3 1 6 3 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .o.............3.o.............3.o............. & | * 8 * * * * * * ♦ 0 3 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 3 0 0 6 3 0 3 6 3 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 3 0 6 1 3 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ..o............3..o............3..o............ & | * * 12 * * * * * ♦ 0 0 2 0 2 0 0 4 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 4 0 4 0 4 2 0 2 1 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 2 2 4 0 0 4 2 2 4 0 0 0 0 0 0 0 0 0 0 0 ...o...........3...o...........3...o........... & | * * * 24 * * * * ♦ 0 0 0 1 0 1 0 2 0 0 2 2 2 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 2 0 1 2 0 2 0 2 2 0 2 2 0 1 1 2 2 2 2 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 2 2 0 1 2 2 0 2 1 1 2 2 2 0 0 0 0 0 0 ....o..........3....o..........3....o.......... & | * * * * 24 * * * ♦ 0 0 0 0 0 0 1 0 1 0 0 2 0 0 0 2 2 2 1 1 0 0 0 0 0 | 0 0 0 0 0 0 0 2 0 1 2 0 0 2 0 2 0 2 0 0 2 2 0 0 0 1 1 2 2 2 2 2 2 1 0 0 0 | 0 0 0 0 0 0 1 2 2 0 1 2 0 2 0 2 0 1 1 2 2 2 0 .....o.........3.....o.........3.....o......... & | * * * * * 24 * * ♦ 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 2 0 0 1 1 1 2 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 2 0 0 1 0 2 0 2 2 0 0 2 0 0 2 4 0 2 1 3 2 2 | 0 0 0 0 0 0 0 0 0 1 2 2 0 0 1 2 2 0 3 0 4 2 1 ......o........3......o........3......o........ & | * * * * * * 8 * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 3 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 6 0 3 0 0 0 3 0 0 6 0 3 0 6 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 3 0 6 1 0 3 0 6 0 .......o.......3.......o.......3.......o....... | * * * * * * * 12 ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 0 0 0 4 0 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 2 0 0 2 0 4 0 4 4 0 0 4 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 4 4 0 0 2 4 4 0 -----------------------------------------------------+----------------------+----------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------- x.............. ............... ............... & | 2 0 0 0 0 0 0 0 | 12 * * * * * * * * * * * * * * * * * * * * * * * * | 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 oo.............3oo.............3oo.............&#x & | 1 1 0 0 0 0 0 0 | * 24 * * * * * * * * * * * * * * * * * * * * * * * | 0 2 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o.o............3o.o............3o.o............&#x & | 1 0 1 0 0 0 0 0 | * * 24 * * * * * * * * * * * * * * * * * * * * * * | 0 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o..o...........3o..o...........3o..o...........&#x & | 1 0 0 1 0 0 0 0 | * * * 24 * * * * * * * * * * * * * * * * * * * * * | 0 0 0 2 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .oo............3.oo............3.oo............&#x & | 0 1 1 0 0 0 0 0 | * * * * 24 * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 2 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .o.o...........3.o.o...........3.o.o...........&#x & | 0 1 0 1 0 0 0 0 | * * * * * 24 * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 1 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 2 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .o..o..........3.o..o..........3.o..o..........&#x & | 0 1 0 0 1 0 0 0 | * * * * * * 24 * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 2 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ..oo...........3..oo...........3..oo...........&#x & | 0 0 1 1 0 0 0 0 | * * * * * * * 48 * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 ..o.o..........3..o.o..........3..o.o..........&#x & | 0 0 1 0 1 0 0 0 | * * * * * * * * 24 * * * * * * * * * * * * * * * * | 0 0 0 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0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 | * * * * * * * * * * * * * * * * 48 * * * * * * ....o...o......3....x...o...... ...............&#x & ♦ 0 0 0 0 3 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 3 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * 8 * * * * * ....ox...o..... ............... ...............&#x & ♦ 0 0 0 0 1 3 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 1 0 0 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 1 0 0 | * * * * * * * * * * * * * * * * * * 24 * * * * ............... ....x..oo...... ...............&#x & ♦ 0 0 0 0 2 0 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 2 0 0 0 0 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 2 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * 24 * * * ....oo.o.o.....3....oo.o.o.....3....oo.o.o.....&#x & ♦ 0 0 0 0 1 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 | * * * * * * * * * * * * * * * * * * * * 48 * * ....o..ooo.....3....o..ooo.....3....o..ooo.....&#x & ♦ 0 0 0 0 1 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 | * * * * * * * * * * * * * * * * * * * * * 48 * .....x...o..... ............... .....o...x.....&#x ♦ 0 0 0 0 0 4 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 | * * * * * * * * * * * * * * * * * * * * * * 6
os3os4oo3fo&#zx → height = 0 o.3o.4o.3o. | 24 * ♦ 12 0 0 | 6 24 0 0 0 | 8 12 0 0 tips of ikepies demi( .o3.o4.o3.o ) | * 96 ♦ 3 3 6 | 3 12 3 9 3 | 6 9 1 4 vertices of sadi ------------------------+-------+-------------+-------------------+-------------- demi( oo3oo4oo3oo&#zx ) | 1 1 | 288 * * | 1 4 0 0 0 | 2 3 0 0 .. .s4.o .. | 0 2 | * 144 * | 1 0 0 2 2 | 0 2 1 2 sefa( .s3.s .. .. ) | 0 2 | * * 288 | 0 2 1 2 0 | 2 2 0 1 ------------------------+-------+-------------+-------------------+-------------- .. os4oo ..&#x | 1 2 | 2 1 0 | 144 * * * * | 0 2 0 0 sefa( os3os .. ..&#x ) | 1 2 | 2 0 1 | * 576 * * * | 1 1 0 0 .s3.s .. .. | 0 3 | 0 0 3 | * * 96 * * | 2 0 0 0 sefa( .s3.s4.o .. ) | 0 3 | 0 1 2 | * * * 288 * | 0 1 0 1 sefa( .. .s4.o3.o ) | 0 3 | 0 3 0 | * * * * 96 | 0 0 1 1 ------------------------+-------+-------------+-------------------+-------------- os3os .. .. ♦ 1 3 | 3 0 3 | 0 3 1 0 0 | 192 * * * sefa( os3os4oo ..&#x ) ♦ 1 3 | 3 1 2 | 1 2 0 1 0 | * 288 * * .. .s4.o3.o ♦ 0 4 | 0 6 0 | 0 0 0 0 4 | * * 24 * sefa( .s3.s4.o3.o ) ♦ 0 4 | 0 3 3 | 0 0 0 3 1 | * * * 96
foxo3ooof3xfoo *b3oxfo&#zx → all heights = 0 o...3o...3o... *b3o... | 32 * * * ♦ 3 3 3 3 0 0 0 0 0 | 3 3 6 3 3 6 6 0 0 0 0 0 0 | 1 1 3 3 6 6 0 0 0 0 .o..3.o..3.o.. *b3.o.. | * 32 * * ♦ 0 3 0 0 3 3 3 0 0 | 0 6 0 0 3 6 0 3 3 3 6 0 0 | 0 3 0 6 0 6 1 1 3 0 ..o.3..o.3..o. *b3..o. | * * 32 * ♦ 0 0 3 0 0 3 0 3 3 | 0 0 3 0 3 0 6 0 6 0 6 3 3 | 0 0 1 0 3 6 0 3 6 1 ...o3...o3...o *b3...o | * * * 24 ♦ 0 0 0 4 0 0 4 0 4 | 0 0 0 2 0 8 8 0 0 2 8 0 2 | 0 0 0 4 4 8 0 0 4 0 ---------------------------+-------------+----------------------------+-------------------------------------------+---------------------------- .... .... x... .... | 2 0 0 0 | 48 * * * * * * * * | 2 0 2 1 0 0 0 0 0 0 0 0 0 | 1 0 2 0 2 0 0 0 0 0 oo..3oo..3oo.. *b3oo..&#x | 1 1 0 0 | * 96 * * * * * * * | 0 2 0 0 1 2 0 0 0 0 0 0 0 | 0 1 0 2 0 2 0 0 0 0 o.o.3o.o.3o.o. *b3o.o.&#x | 1 0 1 0 | * * 96 * * * * * * | 0 0 2 0 1 0 2 0 0 0 0 0 0 | 0 0 1 0 2 2 0 0 0 0 o..o3o..o3o..o *b3o..o&#x | 1 0 0 1 | * * * 96 * * * * * | 0 0 0 1 0 2 2 0 0 0 0 0 0 | 0 0 0 1 2 2 0 0 0 0 .... .... .... .x.. | 0 2 0 0 | * * * * 48 * * * * | 0 2 0 0 0 0 0 2 0 1 0 0 0 | 0 2 0 2 0 0 1 0 0 0 .oo.3.oo.3.oo. *b3.oo.&#x | 0 1 1 0 | * * * * * 96 * * * | 0 0 0 0 1 0 0 0 2 0 2 0 0 | 0 0 0 0 0 2 0 1 2 0 .o.o3.o.o3.o.o *b3.o.o&#x | 0 1 0 1 | * * * * * * 96 * * | 0 0 0 0 0 2 0 0 0 1 2 0 0 | 0 0 0 2 0 2 0 0 1 0 ..x. .... .... .... | 0 0 2 0 | * * * * * * * 48 * | 0 0 0 0 0 0 0 0 2 0 0 2 1 | 0 0 0 0 0 0 0 2 2 1 ..oo3..oo3..oo *b3..oo&#x | 0 0 1 1 | * * * * * * * * 96 | 0 0 0 0 0 0 2 0 0 0 2 0 1 | 0 0 0 0 1 2 0 0 2 0 ---------------------------+-------------+----------------------------+-------------------------------------------+---------------------------- .... o...3x... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 | 32 * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 .... .... .... ox..&#x | 1 2 0 0 | 0 2 0 0 1 0 0 0 0 | * 96 * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0 .... .... x.o. ....&#x | 2 0 1 0 | 1 0 2 0 0 0 0 0 0 | * * 96 * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 .... .... x..o ....&#x | 2 0 0 1 | 1 0 0 2 0 0 0 0 0 | * * * 48 * * * * * * * * * | 0 0 0 0 2 0 0 0 0 0 ooo.3ooo.3ooo. *b3ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 | * * * * 96 * * * * * * * * | 0 0 0 0 0 2 0 0 0 0 oo.o3oo.o3oo.o *b3oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 1 0 0 | * * * * * 192 * * * * * * * | 0 0 0 1 0 1 0 0 0 0 o.oo3o.oo3o.oo *b3o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 1 | * * * * * * 192 * * * * * * | 0 0 0 0 1 1 0 0 0 0 .... .o.. .... *b3.x.. | 0 3 0 0 | 0 0 0 0 3 0 0 0 0 | * * * * * * * 32 * * * * * | 0 1 0 0 0 0 1 0 0 0 .ox. .... .... ....&#x | 0 1 2 0 | 0 0 0 0 0 2 0 1 0 | * * * * * * * * 96 * * * * | 0 0 0 0 0 0 0 1 1 0 .... .... .... .x.o&#x | 0 2 0 1 | 0 0 0 0 1 0 2 0 0 | * * * * * * * * * 48 * * * | 0 0 0 2 0 0 0 0 0 0 .ooo3.ooo3.ooo *b3.ooo&#x | 0 1 1 1 | 0 0 0 0 0 1 1 0 1 | * * * * * * * * * * 192 * * | 0 0 0 0 0 1 0 0 1 0 ..x.3..o. .... .... | 0 0 3 0 | 0 0 0 0 0 0 0 3 0 | * * * * * * * * * * * 32 * | 0 0 0 0 0 0 0 1 0 1 ..xo .... .... ....&#x | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 | * * * * * * * * * * * * 48 | 0 0 0 0 0 0 0 0 2 0 ---------------------------+-------------+----------------------------+-------------------------------------------+---------------------------- .... o...3x... *b3o... ♦ 4 0 0 0 | 6 0 0 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * .... oo.. .... *b3ox..&#x ♦ 1 3 0 0 | 0 3 0 0 3 0 0 0 0 | 0 3 0 0 0 0 0 1 0 0 0 0 0 | * 32 * * * * * * * * .... o.o.3x.o. ....&#x ♦ 3 0 1 0 | 3 0 3 0 0 0 0 0 0 | 1 0 3 0 0 0 0 0 0 0 0 0 0 | * * 32 * * * * * * * .... .... .... ox.o&#x ♦ 1 2 0 1 | 0 2 0 1 1 0 2 0 0 | 0 1 0 0 0 2 0 0 0 1 0 0 0 | * * * 96 * * * * * * .... .... x.oo ....&#x ♦ 2 0 1 1 | 1 0 2 2 0 0 0 0 1 | 0 0 1 1 0 0 2 0 0 0 0 0 0 | * * * * 96 * * * * * oooo3oooo3oooo *b3oooo&#x ♦ 1 1 1 1 | 0 1 1 1 0 1 1 0 1 | 0 0 0 0 1 1 1 0 0 0 1 0 0 | * * * * * 192 * * * * .o..3.o.. .... *b3.x.. ♦ 0 4 0 0 | 0 0 0 0 6 0 0 0 0 | 0 0 0 0 0 0 0 4 0 0 0 0 0 | * * * * * * 8 * * * .ox.3.oo. .... ....&#x ♦ 0 1 3 0 | 0 0 0 0 0 3 0 3 0 | 0 0 0 0 0 0 0 0 3 0 0 1 0 | * * * * * * * 32 * * .oxo .... .... ....&#x ♦ 0 1 2 1 | 0 0 0 0 0 2 1 1 2 | 0 0 0 0 0 0 0 0 1 0 2 0 1 | * * * * * * * * 96 * ..x.3..o.3..o. .... ♦ 0 0 4 0 | 0 0 0 0 0 0 0 6 0 | 0 0 0 0 0 0 0 0 0 0 0 4 0 | * * * * * * * * * 8
xffoo3oxoof3fooxo3ooffx&#zx → all heights = 0 – except those of the not existing lacing(2,4) o....3o....3o....3o.... & | 60 * * ♦ 2 2 2 2 4 0 0 | 1 1 4 6 4 8 2 4 0 0 | 2 2 2 6 8 0 0 .o...3.o...3.o...3.o... & | * 40 * ♦ 0 3 0 3 0 3 3 | 0 3 3 0 6 6 3 0 3 6 | 1 0 6 3 6 1 3 ..o..3..o..3..o..3..o.. | * * 20 ♦ 0 0 6 0 0 0 6 | 0 0 0 0 12 0 6 6 0 6 | 0 0 6 0 12 0 2 ------------------------------+----------+---------------------------+--------------------------------------+------------------------ x.... ..... ..... ..... & | 2 0 0 | 60 * * * * * * | 1 0 2 2 0 0 0 0 0 0 | 2 1 0 2 0 0 0 oo...3oo...3oo...3oo...&#x & | 1 1 0 | * 120 * * * * * | 0 1 0 0 2 2 0 0 0 0 | 0 0 2 1 2 0 0 o.o..3o.o..3o.o..3o.o..&#x & | 1 0 1 | * * 120 * * * * | 0 0 0 0 2 0 1 2 0 0 | 0 0 1 0 4 0 0 o..o.3o..o.3o..o.3o..o.&#x & | 1 1 0 | * * * 120 * * * | 0 0 2 0 0 2 1 0 0 0 | 1 0 0 2 2 0 0 o...o3o...o3o...o3o...o&#x | 2 0 0 | * * * * 120 * * | 0 0 0 2 0 2 0 1 0 0 | 0 1 0 2 2 0 0 ..... .x... ..... ..... & | 0 2 0 | * * * * * 60 * | 0 1 0 0 0 0 0 0 2 2 | 0 0 2 0 0 1 2 .oo..3.oo..3.oo..3.oo..&#x & | 0 1 1 | * * * * * * 120 | 0 0 0 0 2 0 1 0 0 2 | 0 0 2 0 2 0 1 ------------------------------+----------+---------------------------+--------------------------------------+------------------------ x....3o.... ..... ..... & | 3 0 0 | 3 0 0 0 0 0 0 | 20 * * * * * * * * * | 2 0 0 0 0 0 0 ..... ox... ..... .....&#x & | 1 2 0 | 0 2 0 0 0 1 0 | * 60 * * * * * * * * | 0 0 2 0 0 0 0 x..o. ..... ..... .....&#x & | 2 1 0 | 1 0 0 2 0 0 0 | * * 120 * * * * * * * | 1 0 0 1 0 0 0 x...o ..... ..... .....&#x & | 3 0 0 | 1 0 0 0 2 0 0 | * * * 120 * * * * * * | 0 1 0 1 0 0 0 ooo..3ooo..3ooo..3ooo..&#x & | 1 1 1 | 0 1 1 0 0 0 1 | * * * * 240 * * * * * | 0 0 1 0 1 0 0 oo..o3oo..o3oo..o3oo..o&#x & | 2 1 0 | 0 1 0 1 1 0 0 | * * * * * 240 * * * * | 0 0 0 1 1 0 0 o.oo.3o.oo.3o.oo.3o.oo.&#x & | 1 1 1 | 0 0 1 1 0 0 1 | * * * * * * 120 * * * | 0 0 0 0 2 0 0 o.o.o3o.o.o3o.o.o3o.o.o&#x | 2 0 1 | 0 0 2 0 1 0 0 | * * * * * * * 120 * * | 0 0 0 0 2 0 0 ..... .x...3.o... ..... & | 0 3 0 | 0 0 0 0 0 3 0 | * * * * * * * * 40 * | 0 0 0 0 0 1 1 ..... .xo.. ..... .....&#x & | 0 2 1 | 0 0 0 0 0 1 2 | * * * * * * * * * 120 | 0 0 1 0 0 0 1 ------------------------------+----------+---------------------------+--------------------------------------+------------------------ x..o.3o..o. ..... .....&#x & ♦ 3 1 0 | 3 0 0 3 0 0 0 | 1 0 3 0 0 0 0 0 0 0 | 40 * * * * * * x...o ..... ..... o...x&#x ♦ 4 0 0 | 2 0 0 0 4 0 0 | 0 0 0 4 0 0 0 0 0 0 | * 30 * * * * * ..... oxo.. ..... .....&#x & ♦ 1 2 1 | 0 2 1 0 0 1 2 | 0 1 0 0 2 0 0 0 0 1 | * * 120 * * * * ..... ..... ..... oo..x&#x & ♦ 3 1 0 | 1 1 0 2 2 0 0 | 0 0 1 1 0 2 0 0 0 0 | * * * 120 * * * ooo.o3ooo.o3ooo.o3ooo.o&#x & ♦ 2 1 1 | 0 1 2 1 1 0 1 | 0 0 0 0 1 1 1 1 0 0 | * * * * 240 * * ..... .x...3.o...3.o... & ♦ 0 4 0 | 0 0 0 0 0 6 0 | 0 0 0 0 0 0 0 0 4 0 | * * * * * 10 * ..... .xo..3.oo.. .....&#x & ♦ 0 3 1 | 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 1 3 | * * * * * * 40
xfooxo5xofxoo oxofox5ooxofx&#zx → all heights = 0 – except those of the not existing lacing(1,4), lacing(1,5), lacing(1,6), lacing(2,6), and lacing(3,6) o.....5o..... o.....5o..... | 10 * * * * * ♦ 1 1 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 5 5 5 5 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 5 5 5 5 0 0 0 0 0 0 0 0 0 .o....5.o.... .o....5.o.... | * 25 * * * * ♦ 0 0 2 0 2 4 2 2 0 0 0 0 0 0 0 0 0 0 | 1 4 0 0 4 4 2 1 2 4 4 4 0 0 0 0 0 0 0 0 0 0 | 2 0 4 2 2 4 2 4 0 0 0 0 0 ..o...5..o... ..o...5..o... | * * 25 * * * ♦ 0 0 0 2 0 4 0 0 2 2 2 0 0 0 0 0 0 0 | 0 0 1 4 4 2 4 0 0 4 4 0 2 1 4 0 0 0 0 0 0 0 | 0 2 2 4 4 2 0 4 2 0 0 0 0 ...o..5...o.. ...o..5...o.. | * * * 25 * * ♦ 0 0 0 0 0 0 2 0 0 2 0 2 4 2 0 0 0 0 | 0 0 0 0 0 0 0 2 0 4 0 4 1 0 4 2 4 4 1 4 0 0 | 0 0 0 0 2 0 4 4 2 2 4 2 0 ....o.5....o. ....o.5....o. | * * * * 25 * ♦ 0 0 0 0 0 0 0 2 0 0 2 0 4 0 2 2 0 0 | 0 0 0 0 0 0 0 0 1 0 4 4 0 2 4 4 2 0 0 4 4 1 | 0 0 0 0 0 2 2 4 4 4 2 0 2 .....o5.....o .....o5.....o | * * * * * 10 ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 5 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 10 5 5 | 0 0 0 0 0 0 0 0 0 5 5 5 5 --------------------------------+-------------------+-----------------------------------------------------+-------------------------------------------------------------------------+---------------------------------------- x..... ...... ...... ...... | 2 0 0 0 0 0 | 5 * * * * * * * * * * * * * * * * * | 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 5 0 0 0 0 0 0 0 0 0 0 0 ...... x..... ...... ...... | 2 0 0 0 0 0 | * 5 * * * * * * * * * * * * * * * * | 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 5 0 0 0 0 0 0 0 0 0 0 0 0 oo....5oo.... oo....5oo....&#x | 1 1 0 0 0 0 | * * 50 * * * * * * * * * * * * * * * | 1 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 0 2 1 0 0 0 0 0 0 0 0 0 o.o...5o.o... o.o...5o.o...&#x | 1 0 1 0 0 0 | * * * 50 * * * * * * * * * * * * * * | 0 0 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 2 1 2 0 0 0 0 0 0 0 0 0 ...... ...... .x.... ...... | 0 2 0 0 0 0 | * * * * 25 * * * * * * * * * * * * * | 0 2 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 2 0 0 2 0 0 0 0 0 0 0 .oo...5.oo... .oo...5.oo...&#x | 0 1 1 0 0 0 | * * * * * 100 * * * * * * * * * * * * | 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 1 0 1 0 0 0 0 0 .o.o..5.o.o.. .o.o..5.o.o..&#x | 0 1 0 1 0 0 | * * * * * * 50 * * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 0 2 2 0 0 0 0 0 .o..o.5.o..o. .o..o.5.o..o.&#x | 0 1 0 0 1 0 | * * * * * * * 50 * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 0 2 2 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 2 1 2 0 0 0 0 0 ...... ...... ...... ..x... | 0 0 2 0 0 0 | * * * * * * * * 25 * * * * * * * * * | 0 0 0 2 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | 0 1 0 2 2 0 0 0 0 0 0 0 0 ..oo..5..oo.. ..oo..5..oo..&#x | 0 0 1 1 0 0 | * * * * * * * * * 50 * * * * * * * * | 0 0 0 0 0 0 0 0 0 2 0 0 1 0 2 0 0 0 0 0 0 0 | 0 0 0 0 2 0 0 2 1 0 0 0 0 ..o.o.5..o.o. ..o.o.5..o.o.&#x | 0 0 1 0 1 0 | * * * * * * * * * * 50 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 2 0 0 1 2 0 0 0 0 0 0 0 | 0 0 0 0 0 1 0 2 2 0 0 0 0 ...... ...x.. ...... ...... | 0 0 0 2 0 0 | * * * * * * * * * * * 25 * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 2 0 0 0 0 | 0 0 0 0 0 0 2 0 0 0 2 1 0 ...oo.5...oo. ...oo.5...oo.&#x | 0 0 0 1 1 0 | * * * * * * * * * * * * 100 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 | 0 0 0 0 0 0 1 1 1 1 1 0 0 ...o.o5...o.o ...o.o5...o.o&#x | 0 0 0 1 0 1 | * * * * * * * * * * * * * 50 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 0 0 | 0 0 0 0 0 0 0 0 0 1 2 2 0 ....x. ...... ...... ...... | 0 0 0 0 2 0 | * * * * * * * * * * * * * * 25 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 2 0 | 0 0 0 0 0 0 0 0 2 2 0 0 1 ....oo5....oo ....oo5....oo&#x | 0 0 0 0 1 1 | * * * * * * * * * * * * * * * 50 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 | 0 0 0 0 0 0 0 0 0 2 1 0 2 ...... ...... .....x ...... | 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * 5 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 | 0 0 0 0 0 0 0 0 0 0 0 0 5 ...... ...... ...... .....x | 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0 0 0 0 0 0 0 0 0 | * * * 18 * * * * * * * * * * * * * * * * * * * * * * * * * oo.oo.....3oo.oo..... oo.oo.....3oo.oo.....&#x ♦ 1 1 0 1 1 0 0 0 0 0 | 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 36 * * * * * * * * * * * * * * * * * * * * * * * * o.ooo.....3o.ooo..... o.ooo.....3o.ooo.....&#x ♦ 1 0 1 1 1 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 36 * * * * * * * * * * * * * * * * * * * * * * * .......... .o..x..... .x..o..... ..........&#x ♦ 0 2 0 0 2 0 0 0 0 0 | 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 9 * * * * * * * * * * * * * * * * * * * * * * .......... 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * 9 * * * * * * * * * * * * * * * * * * ..ox..o... .......... .......... ..........&#x ♦ 0 0 1 2 0 0 1 0 0 0 | 0 0 0 0 0 0 0 0 0 2 0 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * 18 * * * * * * * * * * * * * * * * * .......... .......... ..o.o.x... ..........&#x ♦ 0 0 1 0 1 0 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * 18 * * * * * * * * * * * * * * * * ..ooo.o...3..ooo.o... ..ooo.o...3..ooo.o...&#x ♦ 0 0 1 1 1 0 1 0 0 0 | 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * 36 * * * * * * * * * * * * * * * .......... .......... .......... ...o.x.o..&#x ♦ 0 0 0 1 0 2 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * 18 * * * * * * * * * * * * * * ...x..oo.. .......... .......... ..........&#x ♦ 0 0 0 2 0 0 1 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * 18 * * * * * * * * * * * * * ...oooo...3...oooo... ...oooo...3...oooo...&#x ♦ 0 0 0 1 1 1 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * 36 * * * * * * * * * * * * ...o.ooo..3...o.ooo.. ...o.ooo..3...o.ooo..&#x ♦ 0 0 0 1 0 1 1 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * 36 * * * * * * * * * * * .......... ....xo..o. .......... ..........&#x ♦ 0 0 0 0 2 1 0 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * 18 * * * * * * * * * * .......... .......... ....o.x.o. ..........&#x ♦ 0 0 0 0 1 0 2 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 1 0 2 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * 18 * * * * * * * * * ....ooo.o.3....ooo.o. ....ooo.o.3....ooo.o.&#x ♦ 0 0 0 0 1 1 1 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * 36 * * * * * * * * .......... .....o.x.. .......... .....x.o..&#x ♦ 0 0 0 0 0 2 0 2 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 0 0 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * 9 * * * * * * * .......... .....o.x.o .......... ..........&#x ♦ 0 0 0 0 0 1 0 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 1 2 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 0 1 0 0 | * * * * * * * * * * * * * * * * * * * * * * 18 * * * * * * .....ooo.o3.....ooo.o .....ooo.o3.....ooo.o&#x ♦ 0 0 0 0 0 1 1 1 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * 36 * * * * * .....oo.oo3.....oo.oo .....oo.oo3.....oo.oo&#x ♦ 0 0 0 0 0 1 1 0 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * 36 * * * * ......o.x. .......... ......x.o. ..........&#x ♦ 0 0 0 0 0 0 2 0 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 0 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * * 9 * * * ......o.xo .......... .......... ..........&#x ♦ 0 0 0 0 0 0 1 0 2 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 1 | * * * * * * * * * * * * * * * * * * * * * * * * * * 18 * * .......o.o3.......x.o .......... ..........&#x ♦ 0 0 0 0 0 0 0 3 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * * * * 6 * ........xo3........oo .......... ..........&#x ♦ 0 0 0 0 0 0 0 0 3 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 | * * * * * * * * * * * * * * * * * * * * * * * * * * * * 6
xofFoxFf(oV)... 2 ooxofoof(xo)... 5 oxooofxo(xo)... &#xt (where "..." means continuation of layers A-H in reverse order within pap-symmetry) (line || pseudo ortho {5} || pseudo gyro (f,x)-pip || pseudo F-line || pseudo gyro ortho f-{5} || pseudo (x,f)-pip || pseudo (F,x)-pip || pseudo gyro f-pip || ( pseudo ortho {10} + pseudo V-line ) || pseudo f-pip || pseudo gyro (F,x)-pip || pseudo gyro (x,f)-pip || pseudo ortho f-{5} || pseudo F-line || pseudo (f,x)-pip || pseudo ortho gyro {5} || line) → height(A,B) = height(C,D) = height(E,F) = height(G,H) = sqrt[(5-2 sqrt(5))/20] = 0.162460 height(B,C) = height(F,G) = height(H,I) = height(H,i) = sqrt[(5-sqrt(5))/40] = 0.262866 height(D,E) = sqrt[(25-11 sqrt(5))/40] = 0.100406 (= diff. of former ones) o.......(..)... 2 o.......(..)... 5 o.......(..)... & | 4 * * * * * * * * * ♦ 1 5 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 5 5 10 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 5 5 5 5 0 0 0 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