Acronym cubaike, cube || ike, K-4.21 Name cube atop icosahedron Segmentochoron display Circumradius 1 Coordinates (1/2, 1/2, 1/2; 1/2)       & all changes of sign in first 3 coords (top cube) (τ/2, 1/2, 0; -τ-1/2)       & even permutations in first 3 coords, all changes of sign in first 3 coords (bottom ike) where τ = (1+sqrt(5))/2; circumcenter here would be at origin Dihedral angles at {3} between squippy and tet:   arccos[-(3 sqrt(5)-1)/8] = 135.522488° at {4} between cube and trip:   arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157° at {3} between ike and tet:   arccos[-sqrt(7-3 sqrt(5))/4] = 97.761244° at {3} between ike and squippy:   arccos[sqrt(7-3 sqrt(5))/4] = 82.238756° at {3} between squippy and trip:   ... at {4} between squippy and trip:   ... Confer related CRFs: pta cubaike   ptaika cube   baucubaike   general polytopal classes: segmentochora Externallinks

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
```