Acronym ...
Name external blend of the square-antiprism prism and 2 squap-pyramids,
squap-pyramid-biaugmented square-antiprism prism
  
 ©
Lace city
in approx. ASCII-art 
    x4o     x4o    	-- x x4o (cube)
                   
o4o             o4o
                   
    o4x     o4x    	-- x o4x (gyro cube)

     |       |
     |       +-- s2s4s (squap)
     +---------- s2s4s (squap)
Dihedral angles
  • at {3} between tet and tet:   arccos[(1-3 sqrt(2))/4] = 144.160482°
  • at {4} between cube and squippy:   arccos[-sqrt[4-sqrt(2)]/2] = 143.515624°
  • at {3} between tet and trip:   arccos(-sqrt[12-3 sqrt(2)]/4) = 134.130974°
  • at {4} between trip and trip:   arccos[(1-2 sqrt(2))/3] = 127.551603°
  • at {3} between squippy and tet:   arccos[(2-3 sqrt(2))/4] = 124.101465°
  • at {4} between cube and trip:   arccos[(1-sqrt(2))/sqrt(3)] = 103.836160°
Face vector 18, 56, 68, 30
Confer
general polytopal classes:
CRF  

Incidence matrix

16 * | 1  2  2  1 | 2 2 1  3  2  2 | 1 3 1  3
 * 2 | 0  0  0  8 | 0 0 0  0  8  8 | 0 0 2  8  verf: squap
-----+------------+----------------+---------
 2 0 | 8  *  *  * | 2 2 0  0  0  0 | 1 3 0  0  prism lacings
 2 0 | * 16  *  * | 1 0 1  1  1  0 | 1 1 1  1  base sides
 2 0 | *  * 16  * | 0 1 0  2  0  1 | 0 2 0  2  antiprism lacings
 1 1 | *  *  * 16 | 0 0 0  0  2  2 | 0 0 1  3  pyramid lacings
-----+------------+----------------+---------
 4 0 | 2  2  0  0 | 8 * *  *  *  * | 1 1 0  0
 4 0 | 2  0  2  0 | * 8 *  *  *  * | 0 2 0  0
 4 0 | 0  4  0  0 | * * 4  *  *  * | 1 0 1  0
 3 0 | 0  1  2  0 | * * * 16  *  * | 0 1 0  1
 2 1 | 0  1  0  2 | * * *  * 16  * | 0 0 1  1
 2 1 | 0  0  1  2 | * * *  *  * 16 | 0 0 0  2
-----+------------+----------------+---------
 8 0 | 4  8  0  0 | 4 0 2  0  0  0 | 2 * *  *  cube
 6 0 | 3  2  4  0 | 1 2 0  2  0  0 | * 8 *  *  trip
 4 1 | 0  4  0  4 | 0 0 1  0  4  0 | * * 4  *  squippy
 3 1 | 0  1  2  3 | 0 0 0  1  1  2 | * * * 16  tet

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