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Acronym
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...
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Name
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(1,0,4,12,0)-diminished vertex-first-rotunda of ex,
heptadeca-diminished vertex-first rotunda of hexacosachoron
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 ©
turquois: mibdies, lilac: teddies, purple: ike, remainder: tets, missing: outermost id
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Circumradius
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(1+sqrt(5))/2 = 1.618034
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Lace city
in approx. ASCII-art
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x3o o3f f3o o3x
o3f f3x demi(x3f) f3o o3o
(F=ff)
o3x x3f F3o f3f o3F f3x x3o
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Face vector
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58, 204, 214, 68
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Confer
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- segmentochora:
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ike || doe
doe || id
- other CRFs:
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rotunda of ex
pt || ike || doe || id
ike || doe || id
ike || cube-dim-doe || id
- uniform relative:
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ex
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The medial section here is the tetrahedrally diminished dodecahedron.
From that section the whole polychoron inherits its chirality.
Incidence matrix
ike || pseudo tet-dim-doe || id → height(1,2) = 1/2, height(2,3) = (1+sqrt(5))/4 = 0.809017
12 * * * * * | 2 1 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 3 1 2 2 2 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 3 1 1 2 1 0 0 0 all ike level vertices
* 12 * * * * | 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 | 0 0 0 1 1 1 0 2 2 1 1 1 1 1 1 1 0 0 0 0 0 | 0 1 1 0 1 1 3 1 0 0 B-doe / dim.vertices of doe level
* * 4 * * * | 0 0 0 0 0 0 3 0 3 0 0 0 3 0 0 0 0 0 | 0 0 0 0 0 0 3 0 0 3 3 0 3 0 0 0 3 0 0 0 0 | 0 0 0 1 0 3 3 0 1 0 C-doe / isol. vertices of doe level, verf: teddi
* * * 12 * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 2 1 1 0 0 | 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 0 1 2 1 0 | 0 1 0 0 0 0 2 1 0 1 A-id / tetrahedral triangle vertices of id level
* * * * 6 * | 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 0 | 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 2 0 0 2 2 0 | 0 0 0 0 0 0 2 2 0 1 B-id / isol. / octahedral vertices of id level
* * * * * 12 | 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 2 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 2 0 2 1 1 | 0 0 0 0 0 0 2 1 1 1 C-id / other tetrahedral triangle vertices of id level
----------------+-----------------------------------------------------+-----------------------------------------------------------+------------------------
2 0 0 0 0 0 | 12 * * * * * * * * * * * * * * * * * | 1 1 0 1 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 A/B-edge of ike layer
2 0 0 0 0 0 | * 6 * * * * * * * * * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 2 0 1 0 0 0 0 0 B/B-edge of ike layer
2 0 0 0 0 0 | * * 12 * * * * * * * * * * * * * * * | 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 1 0 0 0 0 B/C-edge of ike layer
1 1 0 0 0 0 | * * * 12 * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 0 1 0 1 0 0 0 with adj. {5}, near bottom B vertex of doe-layer trapezium
1 1 0 0 0 0 | * * * * 12 * * * * * * * * * * * * * | 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 0 0 1 1 0 0 0 with adj. {5}, near bottom C vertex of doe-layer trapezium
1 1 0 0 0 0 | * * * * * 12 * * * * * * * * * * * * | 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 1 1 0 0 0 w/o adj. {5}
1 0 1 0 0 0 | * * * * * * 12 * * * * * * * * * * * | 0 0 0 0 0 0 2 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 0 2 1 0 0 0
0 2 0 0 0 0 | * * * * * * * 6 * * * * * * * * * * | 0 0 0 0 0 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 0
0 1 1 0 0 0 | * * * * * * * * 12 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 2 0 0 0
0 1 0 1 0 0 | * * * * * * * * * 12 * * * * * * * * | 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 0 0 0 0 0 | 0 1 0 0 0 0 2 1 0 0
0 1 0 0 1 0 | * * * * * * * * * * 12 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 | 0 0 0 0 0 0 2 1 0 0
0 1 0 0 0 1 | * * * * * * * * * * * 12 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 0 0 0 0 2 1 0 0
0 0 1 0 0 1 | * * * * * * * * * * * * 12 * * * * * | 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 0 0 2 0 1 0
0 0 0 2 0 0 | * * * * * * * * * * * * * 12 * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 | 0 1 0 0 0 0 1 0 0 1
0 0 0 1 1 0 | * * * * * * * * * * * * * * 12 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 0 0 0 0 1 1 0 1
0 0 0 1 0 1 | * * * * * * * * * * * * * * * 12 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 0 0 0 0 1 1 0 1
0 0 0 0 1 1 | * * * * * * * * * * * * * * * * 12 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 0 0 0 1 1 0 1
0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 | 0 0 0 0 0 0 1 0 1 1
----------------+-----------------------------------------------------+-----------------------------------------------------------+------------------------
3 0 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 A-{3} of ike layer
3 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 12 * * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 B-{3} of ike layer
3 0 0 0 0 0 | 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 0 C-{3} of ike layer
2 1 0 0 0 0 | 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 12 * * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 dangling from A/B-edge of ike layer
2 1 0 0 0 0 | 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 12 * * * * * * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 dangling from B/B-edge of ike layer
2 1 0 0 0 0 | 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 12 * * * * * * * * * * * * * * * | 0 0 1 0 0 1 0 0 0 0 dangling from B/C-edge of ike layer
2 0 1 0 0 0 | 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 12 * * * * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 0
1 2 0 2 0 0 | 0 0 0 1 1 0 0 0 0 2 0 0 0 1 0 0 0 0 | * * * * * * * 12 * * * * * * * * * * * * * | 0 1 0 0 0 0 1 0 0 0 lacing {5}
1 2 0 0 0 0 | 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * 12 * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0
1 1 1 0 0 0 | 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 12 * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 above bottom B/C-edge of doe-layer trapezium
1 1 1 0 0 0 | 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * 12 * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 above lateral B/C-edge of doe-layer trapezium
0 2 0 0 1 0 | 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 | * * * * * * * * * * * 6 * * * * * * * * * | 0 0 0 0 0 0 2 0 0 0
0 1 1 0 0 1 | 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | * * * * * * * * * * * * 12 * * * * * * * * | 0 0 0 0 0 0 2 0 0 0
0 1 0 1 1 0 | 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 | * * * * * * * * * * * * * 12 * * * * * * * | 0 0 0 0 0 0 1 1 0 0
0 1 0 1 0 1 | 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 | * * * * * * * * * * * * * * 12 * * * * * * | 0 0 0 0 0 0 1 1 0 0
0 1 0 0 1 1 | 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 | * * * * * * * * * * * * * * * 12 * * * * * | 0 0 0 0 0 0 1 1 0 0
0 0 1 0 0 2 | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 | * * * * * * * * * * * * * * * * 12 * * * * | 0 0 0 0 0 0 1 0 1 0
0 0 0 3 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 | * * * * * * * * * * * * * * * * * 4 * * * | 0 1 0 0 0 0 0 0 0 1
0 0 0 2 1 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 | * * * * * * * * * * * * * * * * * * 12 * * | 0 0 0 0 0 0 1 0 0 1 bottom {5}
0 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 | * * * * * * * * * * * * * * * * * * * 12 * | 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 1 1
----------------+-----------------------------------------------------+-----------------------------------------------------------+------------------------
12 0 0 0 0 0 | 12 6 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 12 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * ike (top layer)
3 3 0 3 0 0 | 3 0 0 3 3 0 0 0 0 3 0 0 0 3 0 0 0 0 | 1 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 0 0 | * 4 * * * * * * * * teddi (A vertical)
3 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 12 * * * * * * * tet (upper B vertical)
3 0 1 0 0 0 | 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 4 * * * * * * tet (upper C vertical)
2 2 0 0 0 0 | 0 1 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 6 * * * * * tet (underneath top B/B-edge)
2 1 1 0 0 0 | 0 0 1 0 1 1 2 0 1 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | * * * * * 12 * * * * tet (underneath top B/C-edge)
1 3 1 2 1 2 | 0 0 0 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 | 0 0 0 0 0 0 0 1 1 1 1 1 2 1 1 1 1 0 1 0 0 | * * * * * * 12 * * * mibdi
0 1 0 1 1 1 | 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 | * * * * * * * 12 * * tet (atop bottom ABC {3})
0 0 1 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 1 | * * * * * * * * 4 * tet (lower C vertical)
0 0 0 12 6 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 12 12 12 12 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 12 12 4 | * * * * * * * * * 1 id (bottom layer)