Movatterモバイル変換

Acronym	cubaike, cube || ike, K-4.21
Name	cube atopicosahedron
Segmentochoron display /VRML	⭳
Circumradius	1
Coordinates	(1/2, 1/2, 1/2; 1/2)       & all changes of sign in first 3 coords (topcube) (τ/2, 1/2, 0; -τ-1/2)       & even permutations in first 3 coords, all changes of sign in first 3 coords (bottomike) where τ = (1+sqrt(5))/2; circumcenter here would be at origin
Dihedral angles	at {3} betweensquippy andtet:   arccos[-(3 sqrt(5)-1)/8] = 135.522488° at {4} betweencube andtrip:   arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157° at {3} betweenike andtet:   arccos[-sqrt(7-3 sqrt(5))/4] = 97.761244° at {3} betweenike andsquippy:   arccos[sqrt(7-3 sqrt(5))/4] = 82.238756° at {3} betweensquippy andtrip:   ... at {4} betweensquippy andtrip:   ...
Face vector	20, 66, 74, 28
Confer	relatedCRFs: pta cubaike  ptaika cube  baucubaike   relatedblends: hocubasiddo   general polytopal classes: segmentochora
External links

Thissegmentochoron is specialin that the bases belong todifferent symmetries, i.e. to C₃ (cube =o3o4x) vs. H₃ (ike =x3o5o).

As abstract polytope it is isomorphic tocubagike, thereby replacingike bygike.

Incidence matrix according toDynkin 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 0demi( .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 0demi( 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 1sefa( .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 0demi( .. .. xo    ) | 2  1 |  1  2 0  0 | * 12  *  *  * * | 0 1  1 0 0sefa( .. os4xo&#x ) | 2  2 |  1  2 1  0 | *  * 12  *  * * | 0 1  1 0 0sefa( os3os ..&#x ) | 1  2 |  0  2 0  1 | *  *  * 24  * * | 0 0  1 1 0sefa( .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 | * *  * * 1starting figure:ox3ox4xo&#x (which as a throughout unit-edged figure could be realized within hyperbolic space only)

cube||ike → height = (1+sqrt(5))/4 = 0.8090178  * |  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 01  1 |  * 24 *  * | 0  1  1  2  0 0 | 0 1  2 1 00  2 |  *  * 6  * | 0  0  2  0  2 0 | 0 1  2 0 10  2 |  *  * * 24 | 0  0  0  1  1 1 | 0 0  1 1 1-----+------------+-----------------+-----------4  0 |  4  0 0  0 | 6  *  *  *  * * | 1 1  0 0 02  1 |  1  2 0  0 | * 12  *  *  * * | 0 1  1 0 02  2 |  1  2 1  0 | *  * 12  *  * * | 0 1  1 0 01  2 |  0  2 0  1 | *  *  * 24  * * | 0 0  1 1 00  3 |  0  0 1  2 | *  *  *  * 12 * | 0 0  1 0 10  3 |  0  0 0  3 | *  *  *  *  * 8 | 0 0  0 1 1-----+------------+-----------------+-----------8  0 | 12  0 0  0 | 6  0  0  0  0 0 |1 *  * * *cube4  2 |  4  4 1  0 | 1  2  2  0  0 0 | * 6  * * *trip2  3 |  1  4 1  2 | 0  1  1  2  1 0 | * * 12 * *squippy1  3 |  0  3 0  3 | 0  0  0  3  0 1 | * *  * 8 *tet0 12 |  0  0 6 24 | 0  0  0  0 12 8 | * *  * *1ike

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) = 0o(...) 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 0o(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 0o(.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 0o(..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 0x(...) .(...) 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 0x(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 0o(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 0o(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 0o(.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 0x(..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 * * * * * * * *cubex(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 * * * * * *squippyo(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 * * * * *tetx(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 * *squippyx(..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 | * * * * * * * *1ike