Acronym cubaike, cube || ike, K-4.21
Name cube atop icosahedron
 
Segmentochoron display
Circumradius 1
Coordinates
  1. (1/2, 1/2, 1/2; 1/2)       & all changes of sign in first 3 coords
    (top cube)
  2. (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  
general polytopal classes:
segmentochora  

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

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