Acronym | cubaike, cube || ike, K-4.21 |
Name | cube atop icosahedron |
Segmentochoron display | |
Circumradius | 1 |
Coordinates | where τ = (1+sqrt(5))/2; circumcenter here would be at origin |
Dihedral angles |
|
Face vector | 20, 66, 74, 28 |
Confer |
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External links |
This segmentochoron is special in that the bases belong to different symmetries, i.e. to C3 (cube = o3o4x) vs. H3 (ike = x3o5o).
Incidence matrix according to Dynkin symbol
os3os4xo&#x → height = (1+sqrt(5))/4 = 0.809017
(cube || ike)
o.3o.4o. | 8 * | 3 3 0 0 | 3 3 3 3 0 0 | 1 3 3 1 0
demi( .o3.o4.o ) | * 12 | 0 2 1 4 | 0 1 2 4 3 2 | 0 1 3 2 1
--------------------+------+------------+-----------------+-----------
.. .. x. | 2 0 | 12 * * * | 2 1 1 0 0 0 | 1 2 1 0 0
demi( oo3oo4oo&#x ) | 1 1 | * 24 * * | 0 1 1 2 0 0 | 0 1 2 1 0
.. .s4.o | 0 2 | * * 6 * | 0 0 2 0 2 0 | 0 1 2 0 1
sefa( .s3.s .. ) | 0 2 | * * * 24 | 0 0 0 1 1 1 | 0 0 1 1 1
--------------------+------+------------+-----------------+-----------
.. o.4x. | 4 0 | 4 0 0 0 | 6 * * * * * | 1 1 0 0 0
demi( .. .. xo ) | 2 1 | 1 2 0 0 | * 12 * * * * | 0 1 1 0 0
sefa( .. os4xo&#x ) | 2 2 | 1 2 1 0 | * * 12 * * * | 0 1 1 0 0
sefa( os3os ..&#x ) | 1 2 | 0 2 0 1 | * * * 24 * * | 0 0 1 1 0
sefa( .s3.s4.o ) | 0 3 | 0 0 1 2 | * * * * 12 * | 0 0 1 0 1
.s3.s .. | 0 3 | 0 0 0 3 | * * * * * 8 | 0 0 0 1 1
--------------------+------+------------+-----------------+-----------
o.3o.4x. ♦ 8 0 | 12 0 0 0 | 6 0 0 0 0 0 | 1 * * * *
.. os4xo&#x ♦ 4 2 | 4 4 1 0 | 1 2 2 0 0 0 | * 6 * * *
sefa( os3os4xo&#x ) ♦ 2 3 | 1 4 1 2 | 0 1 1 2 1 0 | * * 12 * *
os3os ..&#x ♦ 1 3 | 0 3 0 3 | 0 0 0 3 0 1 | * * * 8 *
.s3.s4.o ♦ 0 12 | 0 0 6 24 | 0 0 0 0 12 8 | * * * * 1
starting figure: ox3ox4xo&#x (which as a throughout unit-edged figure could be realized within hyperbolic space only)
cube || ike → height = (1+sqrt(5))/4 = 0.809017
8 * | 3 3 0 0 | 3 3 3 3 0 0 | 1 3 3 1 0
* 12 | 0 2 1 4 | 0 1 2 4 3 2 | 0 1 3 2 1
-----+------------+-----------------+-----------
2 0 | 12 * * * | 2 1 1 0 0 0 | 1 2 1 0 0
1 1 | * 24 * * | 0 1 1 2 0 0 | 0 1 2 1 0
0 2 | * * 6 * | 0 0 2 0 2 0 | 0 1 2 0 1
0 2 | * * * 24 | 0 0 0 1 1 1 | 0 0 1 1 1
-----+------------+-----------------+-----------
4 0 | 4 0 0 0 | 6 * * * * * | 1 1 0 0 0
2 1 | 1 2 0 0 | * 12 * * * * | 0 1 1 0 0
2 2 | 1 2 1 0 | * * 12 * * * | 0 1 1 0 0
1 2 | 0 2 0 1 | * * * 24 * * | 0 0 1 1 0
0 3 | 0 0 1 2 | * * * * 12 * | 0 0 1 0 1
0 3 | 0 0 0 3 | * * * * * 8 | 0 0 0 1 1
-----+------------+-----------------+-----------
8 0 | 12 0 0 0 | 6 0 0 0 0 0 | 1 * * * * cube
4 2 | 4 4 1 0 | 1 2 2 0 0 0 | * 6 * * * trip
2 3 | 1 4 1 2 | 0 1 1 2 1 0 | * * 12 * * squippy
1 3 | 0 3 0 3 | 0 0 0 3 0 1 | * * * 8 * tet
0 12 | 0 0 6 24 | 0 0 0 0 12 8 | * * * * 1 ike
x(xfo) x(fox) x(oxf)&#x → height(1,2) = height(1,3) = height(1,4) = (1+sqrt(5))/4 = 0.809017 height(2,3) = height(2,4) = height(3,4) = 0 o(...) o(...) o(...) | 8 * * * | 1 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 1 1 0 .(o..) .(o..) .(o..) | * 4 * * | 0 0 0 2 0 0 1 2 2 0 0 0 | 0 0 0 2 1 2 2 0 0 0 0 0 1 2 2 0 | 0 1 1 2 2 0 0 0 1 .(.o.) .(.o.) .(.o.) | * * 4 * | 0 0 0 0 2 0 0 2 0 1 2 0 | 0 0 0 0 0 2 0 1 2 2 0 0 2 2 0 1 | 0 0 2 2 0 1 1 0 1 .(..o) .(..o) .(..o) | * * * 4 | 0 0 0 0 0 2 0 0 2 0 2 1 | 0 0 0 0 0 0 2 0 0 2 1 2 0 2 1 2 | 0 0 0 2 1 0 2 1 1 -------------------------+---------+-------------------------+---------------------------------+------------------ x(...) .(...) .(...) | 2 0 0 0 | 4 * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0 0 1 0 .(...) x(...) .(...) | 2 0 0 0 | * 4 * * * * * * * * * * | 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 | 1 0 0 0 0 1 1 1 0 .(...) .(...) x(...) | 2 0 0 0 | * * 4 * * * * * * * * * | 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0 1 0 0 0 o(o..) o(o..) o(o..)&#x | 1 1 0 0 | * * * 8 * * * * * * * * | 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 1 0 0 0 0 o(.o.) o(.o.) o(.o.)&#x | 1 0 1 0 | * * * * 8 * * * * * * * | 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 | 0 0 1 1 0 1 1 0 0 o(..o) o(..o) o(..o)&#x | 1 0 0 1 | * * * * * 8 * * * * * * | 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 | 0 0 0 1 1 0 1 1 0 .(x..) .(...) .(...) | 0 2 0 0 | * * * * * * 2 * * * * * | 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 | 0 1 0 0 2 0 0 0 1 .(oo.) .(oo.) .(oo.)&#x | 0 1 1 0 | * * * * * * * 8 * * * * | 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 | 0 0 1 1 0 0 0 0 1 .(o.o) .(o.o) .(o.o)&#x | 0 1 0 1 | * * * * * * * * 8 * * * | 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 0 1 1 0 0 0 1 .(...) .(...) .(.x.) | 0 0 2 0 | * * * * * * * * * 2 * * | 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 | 0 0 2 0 0 1 0 0 1 .(.oo) .(.oo) .(.oo)&#x | 0 0 1 1 | * * * * * * * * * * 8 * | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 0 1 0 0 1 0 1 .(...) .(..x) .(...) | 0 0 0 2 | * * * * * * * * * * * 2 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 | 0 0 0 0 0 0 2 1 1 -------------------------+---------+-------------------------+---------------------------------+------------------ x(...) x(...) .(...) | 4 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * * * | 1 0 0 0 0 0 0 1 0 x(...) .(...) x(...) | 4 0 0 0 | 2 0 2 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 .(...) x(...) x(...) | 4 0 0 0 | 0 2 2 0 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * * * | 1 0 0 0 0 1 0 0 0 x(x..) .(...) .(...)&#x | 2 2 0 0 | 1 0 0 2 0 0 1 0 0 0 0 0 | * * * 4 * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 .(...) .(...) x(o..)&#x | 2 1 0 0 | 0 0 1 2 0 0 0 0 0 0 0 0 | * * * * 4 * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 o(oo.) o(oo.) o(oo.)&#x | 1 1 1 0 | 0 0 0 1 1 0 0 1 0 0 0 0 | * * * * * 8 * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 o(o.o) o(o.o) o(o.o)&#x | 1 1 0 1 | 0 0 0 1 0 1 0 0 1 0 0 0 | * * * * * * 8 * * * * * * * * * | 0 0 0 1 1 0 0 0 0 .(...) x(.o.) .(...)&#x | 2 0 1 0 | 0 1 0 0 2 0 0 0 0 0 0 0 | * * * * * * * 4 * * * * * * * * | 0 0 0 0 0 1 1 0 0 .(...) .(...) x(.x.)&#x | 2 0 2 0 | 0 0 1 0 2 0 0 0 0 1 0 0 | * * * * * * * * 4 * * * * * * * | 0 0 1 0 0 1 0 0 0 o(.oo) o(.oo) o(.oo)&#x | 1 0 1 1 | 0 0 0 0 1 1 0 0 0 0 1 0 | * * * * * * * * * 8 * * * * * * | 0 0 0 1 0 0 1 0 0 x(..o) .(...) .(...)&#x | 2 0 0 1 | 1 0 0 0 0 2 0 0 0 0 0 0 | * * * * * * * * * * 4 * * * * * | 0 0 0 0 1 0 0 1 0 .(...) x(..x) .(...)&#x | 2 0 0 2 | 0 1 0 0 0 2 0 0 0 0 0 1 | * * * * * * * * * * * 4 * * * * | 0 0 0 0 0 0 1 1 0 .(...) .(...) .(ox.)&#x | 0 1 2 0 | 0 0 0 0 0 0 0 2 0 1 0 0 | * * * * * * * * * * * * 4 * * * | 0 0 1 0 0 0 0 0 1 .(ooo) .(ooo) .(ooo)&#x | 0 1 1 1 | 0 0 0 0 0 0 0 1 1 0 1 0 | * * * * * * * * * * * * * 8 * * | 0 0 0 1 0 0 0 0 1 .(x.o) .(...) .(...)&#x | 0 2 0 1 | 0 0 0 0 0 0 1 0 2 0 0 0 | * * * * * * * * * * * * * * 4 * | 0 0 0 0 1 0 0 0 1 .(...) .(.ox) .(...)&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 1 -------------------------+---------+-------------------------+---------------------------------+------------------ x(...) x(...) x(...) | 8 0 0 0 | 4 4 4 0 0 0 0 0 0 0 0 0 | 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * cube x(x..) .(...) x(o..)&#x | 4 2 0 0 | 2 0 2 4 0 0 1 0 0 0 0 0 | 0 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * trip .(...) .(...) x(ox.)&#x | 2 1 2 0 | 0 0 1 2 2 0 0 2 0 1 0 0 | 0 0 0 0 1 2 0 0 1 0 0 0 1 0 0 0 | * * 4 * * * * * * squippy o(ooo) o(ooo) o(ooo)&#x | 1 1 1 1 | 0 0 0 1 1 1 0 1 1 0 1 0 | 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 | * * * 8 * * * * * tet x(x.o) .(...) .(...)&#x | 2 2 0 1 | 1 0 0 2 0 2 1 0 2 0 0 0 | 0 0 0 1 0 0 2 0 0 0 1 0 0 0 1 0 | * * * * 4 * * * * squippy .(...) x(.o.) x(.x.)&#x | 4 0 2 0 | 0 2 2 0 4 0 0 0 0 1 0 0 | 0 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 | * * * * * 2 * * * trip .(...) x(.ox) .(...)&#x | 2 0 1 2 | 0 1 0 0 2 2 0 0 0 0 2 1 | 0 0 0 0 0 0 0 1 0 2 0 1 0 0 0 1 | * * * * * * 4 * * squippy x(..o) x(..x) .(...)&#x | 4 0 0 2 | 2 2 0 0 0 4 0 0 0 0 0 1 | 1 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 | * * * * * * * 2 * trip .(xfo) .(fox) .(oxf)&#zx | 0 4 4 4 | 0 0 0 0 0 0 2 8 8 2 8 2 | 0 0 0 0 0 0 0 0 0 0 0 0 4 8 4 4 | * * * * * * * * 1 ike
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