Acronym pta cubaike
Name cube-augmented cubaike
Circumradius 1
Coordinates
  1. (0, 0, 0; 1)
    (top apex)
  2. (1/2, 1/2, 1/2; 1/2)       & all changes of sign in first 3 coords
    (medial cube section)
  3. (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 {4} between A-squippy and trip:   arccos[-sqrt(5/6)] = 155.905157°
  • at {3} between B-squippy and tet:   arccos[-(3 sqrt(5)-1)/8] = 135.522488°
  • at {3} between A-squippy and A-squippy:   120°
  • at {3} between ike and tet:   arccos[-sqrt(7-3 sqrt(5))/4] = 97.761244°
  • at {3} between ike and B-squippy:   arccos[sqrt(7-3 sqrt(5))/4] = 82.238756°
  • at {3} between B-squippy and trip:   ...
  • at {4} between B-squippy and trip:   ...
Confer
related segmentochora:
cubpy   cubaike  
related CRFs:
ptaika cube  
general polytopal classes:
bistratic lace towers  

Despite of being a mere stack of 2 segmentochora, of cubpy and cubaike, this polychoron is special in that it is still orbiform.


Incidence matrix

point || pseudo cube || ike → height(1,2) = 1/2
                            height(2,3) = (1+sqrt(5))/4 = 0.809017


1 *  * | 8  0  0 0  0 | 12 0  0  0  0  0 0 | 6 0  0 0 0  verf: cube
* 8  * | 1  3  3 0  0 |  3 3  3  3  3  0 0 | 3 3  3 1 0
* * 12 | 0  0  2 1  4 |  0 0  1  2  4  3 2 | 0 1  3 2 1
-------+--------------+--------------------+-----------
1 1  0 | 8  *  * *  * |  3 0  0  0  0  0 0 | 3 0  0 0 0
0 2  0 | * 12  * *  * |  1 2  1  1  0  0 0 | 2 2  1 0 0
0 1  1 | *  * 24 *  * |  0 0  1  1  2  0 0 | 0 1  2 1 0
0 0  2 | *  *  * 6  * |  0 0  0  2  0  2 0 | 0 1  2 0 1
0 0  2 | *  *  * * 24 |  0 0  0  0  1  1 1 | 0 0  1 1 1
-------+--------------+--------------------+-----------
1 2  0 | 2  1  0 0  0 | 12 *  *  *  *  * * | 2 0  0 0 0
0 4  0 | 0  4  0 0  0 |  * 6  *  *  *  * * | 1 1  0 0 0
0 2  1 | 0  1  2 0  0 |  * * 12  *  *  * * | 0 1  1 0 0
0 2  2 | 0  1  2 1  0 |  * *  * 12  *  * * | 0 1  1 0 0
0 1  2 | 0  0  2 0  1 |  * *  *  * 24  * * | 0 0  1 1 0
0 0  3 | 0  0  0 1  2 |  * *  *  *  * 12 * | 0 0  1 0 1
0 0  3 | 0  0  0 0  3 |  * *  *  *  *  * 8 | 0 0  0 1 1
-------+--------------+--------------------+-----------
1 4  0 | 4  4  0 0  0 |  4 1  0  0  0  0 0 | 6 *  * * *  squippy (type A)
0 4  2 | 0  4  4 1  0 |  0 1  2  2  0  0 0 | * 6  * * *  trip
0 2  3 | 0  1  4 1  2 |  0 0  1  1  2  1 0 | * * 12 * *  squippy (type B)
0 1  3 | 0  0  3 0  3 |  0 0  0  0  3  0 1 | * *  * 8 *  tet
0 0 12 | 0  0  0 6 24 |  0 0  0  0  0 12 8 | * *  * * 1  ike

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