Acronym tekah
Name tetrakis hexahedron,
apiculated cube
 
 ©
Inradius 2/sqrt(5) = 0.894427
Vertex figure [t6], [T4]
Coordinates
  1. (2/3, 2/3, 2/3)      & all permutations, all changes of sign
    (vertex inscribed 4/3-cube)
  2. (1, 0, 0)               & all permutations, all changes of sign
    (vertex inscribed sqrt(2)-oct)
Dihedral angles
  • at long edge:   arccos(-4/5) = 143.130102°
  • at short edge:   arccos(-4/5) = 143.130102°
Dual toe
External
links
wikipedia   polytopewiki   mathworld  

The triangles {(t,t,T)} have vertex angles t = arccos(2/3) = 48.189685° resp. T = arccos(1/9) = 83.620630°.

Edge sizes used here are tT = x = 1 (short) resp. tt = b = 4/3 = 1.333333 (long).


Incidence matrix according to Dynkin symbol

m3m4o =
ao3oo4ob&#zx   → height = 0
                 a = sqrt(2) = 1.414214
                 b = 4/3 = 1.333333

o.3o.4o.    | 6 * |  4  0 |  4  [T4]
.o3.o4.o    | * 8 |  3  3 |  6  [t6]
------------+-----+-------+---
oo3oo4oo&#x | 1 1 | 24  * |  2  x
.. .. .b    | 0 2 |  * 12 |  2  b
------------+-----+-------+---
.. .. ob&#x | 1 2 |  2  1 | 24  {(t,t,T)}

m3m3m =
coo3oao3ooc&#z(x,x,b)   → height = 0
                          a = sqrt(2) = 1.414214
                          b = lacing(1,3) = 4/3 = 1.333333
                          c = 4 sqrt(2)/3 = 1.885618

o..3o..3o..           | 4 * * |  3  3  0 |  6  [t6]
.o.3.o.3.o.           | * 6 * |  2  0  2 |  4  [T4]
..o3..o3..o           | * * 4 |  0  3  3 |  6  [t6]
----------------------+-------+----------+---
oo.3oo.3oo.&#x        | 1 1 0 | 12  *  * |  2  x
o.o3o.o3o.o&#b        | 1 0 1 |  * 12  * |  2  b
.oo3.oo3.oo&#x        | 0 1 1 |  *  * 12 |  2  x
----------------------+-------+----------+---
ooo3ooo3ooo&#r(x,x,b) | 1 1 1 |  1  1  1 | 24  {(t,t,T)}

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