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Acronym
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...
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Name
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(1,0,8,12,0)-diminished vertex-first-rotunda of ex,
(subsymmetrical) icosiena-diminished vertex-first rotunda of hexacosachoron
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 ©
green: lying teddies, lilac: vertical teddies, turquois: 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
demi demi
o3f (f3x) (x3f) f3o
(F=ff)
o3x x3f F3o f3f o3F f3x x3o
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o2x f2o x2f f2o o2x
x2o o2F F2x o2F x2o
(F=ff)
(V=2f)
o2o f2x x2F F2f Vo2oV F2f x2F f2x o2o
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Face vector
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54, 168, 166, 52
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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 || tet-dim-doe || id
ike || f-ike || id
- uniform relative:
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ex
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The medial section here is the cubically diminished dodecahedron.
From that section the whole polychoron inherits its chirality.
Note that there are different known icosiena-diminishings of rotunda of ex.
This (1,0,8,12,0)-diminishing is an axially subsymmetrical one (showing up pyritohedral around-symmetry only).
But there is also the (1,0,20,0,0)-diminished vertex-first-rotunda of ex
(ike || f-ike || id), which has full icosahedral around-symmetry.
Incidence matrix
ike || pseudo cube-dim-doe || id → height(1,2) = 1/2, height(2,3) = (1+sqrt(5))/4 = 0.809017
12 * * * | 4 1 1 2 0 0 0 0 0 0 | 2 3 4 2 2 1 0 0 0 0 0 0 | 1 2 3 1 1 0 0 top layer vertices
* 12 * * | 0 0 1 2 1 2 1 0 0 0 | 0 0 2 1 4 2 1 1 2 0 0 0 | 0 2 1 1 3 1 0 medial layer vertices
* * 24 * | 0 0 0 0 0 1 0 2 1 1 | 0 0 0 0 2 0 0 1 1 2 1 1 | 0 1 0 0 2 1 1 A-type botom layer vertices
* * * 6 | 0 0 0 0 0 0 2 0 0 4 | 0 0 0 0 0 0 1 0 4 2 0 2 | 0 0 0 0 2 2 1 B-type botom layer vertices
-----------+-----------------------------+----------------------------------+-----------------
2 0 0 0 | 24 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 top layer edges of teddies
2 0 0 0 | * 6 * * * * * * * * | 0 2 0 2 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0 other top layer edges
1 1 0 0 | * * 12 * * * * * * * | 0 0 2 0 2 0 0 0 0 0 0 0 | 0 2 1 0 1 0 0 upper lacing edges towards acute mid-layer triangle
1 1 0 0 | * * * 24 * * * * * * | 0 0 1 1 1 1 0 0 0 0 0 0 | 0 1 1 1 1 0 0 lacings of dangling tet
0 2 0 0 | * * * * 6 * * * * * | 0 0 0 0 0 2 1 0 0 0 0 0 | 0 0 0 1 2 0 0
0 1 1 0 | * * * * * 24 * * * * | 0 0 0 0 2 0 0 1 1 0 0 0 | 0 1 0 0 2 1 0
0 1 0 1 | * * * * * * 12 * * * | 0 0 0 0 0 0 1 0 2 0 0 0 | 0 0 0 0 2 1 0
0 0 2 0 | * * * * * * * 24 * * | 0 0 0 0 1 0 0 0 0 1 1 0 | 0 1 0 0 1 0 1 bottom {5} lower laterals
0 0 2 0 | * * * * * * * * 12 * | 0 0 0 0 0 0 0 1 0 1 0 1 | 0 0 0 0 1 1 1 bottom {5} base
0 0 1 1 | * * * * * * * * * 24 | 0 0 0 0 0 0 0 0 1 1 0 1 | 0 0 0 0 1 1 1 bottom {5} upper laterals
-----------+-----------------------------+----------------------------------+-----------------
3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * | 1 1 0 0 0 0 0 top layer {3} of teddies
3 0 0 0 | 2 1 0 0 0 0 0 0 0 0 | * 12 * * * * * * * * * * | 1 0 1 0 0 0 0
2 1 0 0 | 1 0 1 1 0 0 0 0 0 0 | * * 24 * * * * * * * * * | 0 1 1 0 0 0 0
2 1 0 0 | 0 1 0 2 0 0 0 0 0 0 | * * * 12 * * * * * * * * | 0 0 1 1 0 0 0
1 2 2 0 | 0 0 1 1 0 2 0 1 0 0 | * * * * 24 * * * * * * * | 0 1 0 0 1 0 0 lacing {5}
1 2 0 0 | 0 0 0 2 1 0 0 0 0 0 | * * * * * 12 * * * * * * | 0 0 0 1 1 0 0
0 2 0 1 | 0 0 0 0 1 0 2 0 0 0 | * * * * * * 6 * * * * * | 0 0 0 0 2 0 0
0 1 2 0 | 0 0 0 0 0 2 0 0 1 0 | * * * * * * * 12 * * * * | 0 0 0 0 1 1 0
0 1 1 1 | 0 0 0 0 0 1 1 0 0 1 | * * * * * * * * 24 * * * | 0 0 0 0 1 1 0
0 0 4 1 | 0 0 0 0 0 0 0 2 1 2 | * * * * * * * * * 12 * * | 0 0 0 0 1 0 1 bottom {5}
0 0 3 0 | 0 0 0 0 0 0 0 3 0 0 | * * * * * * * * * * 8 * | 0 1 0 0 0 0 1
0 0 2 1 | 0 0 0 0 0 0 0 0 1 2 | * * * * * * * * * * * 12 | 0 0 0 0 0 1 1
-----------+-----------------------------+----------------------------------+-----------------
12 0 0 0 | 24 6 0 0 0 0 0 0 0 0 | 8 12 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * top ike
3 3 3 0 | 3 0 3 3 0 3 0 3 0 0 | 1 0 3 0 3 0 0 0 0 0 1 0 | * 8 * * * * * vertical teddi
3 1 0 0 | 2 1 1 2 0 0 0 0 0 0 | 0 1 2 1 0 0 0 0 0 0 0 0 | * * 12 * * * * top-down tet
2 2 0 0 | 0 1 0 4 1 0 0 0 0 0 | 0 0 0 2 0 2 0 0 0 0 0 0 | * * * 6 * * * dangling tet
1 3 4 1 | 0 0 1 2 1 4 2 2 1 2 | 0 0 0 0 2 1 1 1 2 1 0 0 | * * * * 12 * * lying teddi
0 1 2 1 | 0 0 0 0 0 2 1 0 1 2 | 0 0 0 0 0 0 0 1 2 0 0 1 | * * * * * 12 * bottom-up tet
0 0 24 6 | 0 0 0 0 0 0 0 24 12 24 | 0 0 0 0 0 0 0 0 0 12 8 12 | * * * * * * 1 bottom id