Acronym dusidpith
Name small-prismated-tesseractihexadecachoron dual,
triangular antitegmatic hexacontatetrachoron
  
 ©  
Coordinates
  1. (1, 0, 0, 0)                               & all permutations, all changes of sign
    (vertex-inscribed q3o3o4o (q-hex)
  2. (1, 1, 0, 0)/sqrt(2)                   & all permutations, all changes of sign
    (vertex-inscribed o3x3o4o (ico)
  3. (1, 1, 1, 0) [1+2 sqrt(2)]/7       & all permutations, all changes of sign
    (vertex-inscribed o3o3a4o (a-rit)
  4. (1, 1, 1, 1) [2+3 sqrt(2)]/14     & all changes of sign
    (vertex-inscribed o3o3o4b (b-tes)
Dual sidpith
Face vector 80, 208, 192, 64
Confer
general polytopal classes:
Catalan polychora  
External
links 		polytopewiki   quickfur
©

This polychoron can be obtained as the convex hull of a q-hex, a unit ico, an a-rit, and a b-tes, where a = [4+sqrt(2)]/7 = 0.773459 and b = [2+3 sqrt(2)]/7 = 0.891806. (All of those sizes so far just describe pseudo edges only.) Edges then occur between the first two with size c = sqrt[2-sqrt(2)] = 0.765367, between second and third with size d = sqrt[20-2 sqrt(2)]/7 = 0.591980, and between the last two with size e = sqrt[7+3 sqrt(2)]/7 = 0.479001. Faces all are deltoidal tetragons with sides c (red) and d (blue) or with sides d (blue) and e (green), while cells all are identical 3-fold axial deltoidal hexahedra (shown on the right) and have 3 edges of size c, 6 of size d, and 3 of size e.


Incidence matrix according to Dynkin symbol

m3o3o4m =
qooo3oxoo3ooao4ooob&#(c,d,e)   → height = 0
                                 a = [4+sqrt(2)]/7        = 0.773459, 
                                 b = [2+3 sqrt(2)]/7      = 0.891806,
                                 c = sqrt[2-sqrt(2)]      = 0.765367,
                                 d = sqrt[20-2 sqrt(2)]/7 = 0.591980,
                                 e = sqrt[7+3 sqrt(2)]/7  = 0.479001

o...3o...3o...4o...          | 8  *  *  * ♦  6  0  0 | 12  0 |  8  (type a.)
.o..3.o..3.o..4.o..          | * 24  *  * ♦  2  4  0 |  8  4 |  8  (type b.)
..o.3..o.3..o.4..o.          | *  * 32  * ♦  0  3  2 |  3  6 |  6  (type c.)
...o3...o3...o4...o          | *  *  * 16 ♦  0  0  4 |  0  6 |  4  (type d.)
-----------------------------+------------+----------+-------+---
oo..3oo..3oo..4oo..&#c       | 1  1  0  0 | 48  *  * |  4  0 |  4  (red)
.oo.3.oo.3.oo.4.oo.&#d       | 0  1  1  0 |  * 96  * |  2  2 |  4  (blue)
..oo3..oo3..oo4..oo&#e       | 0  0  1  1 |  *  * 64 |  0  3 |  3  (green)
-----------------------------+------------+----------+-------+---
ooo.3ooo.3ooo.4ooo.&#(c,d)   | 1  2  1  0 |  2  2  0 | 96  * |  2  {(ccdd)}
.ooo3.ooo3.ooo4.ooo&#(d,e)   | 0  1  2  1 |  0  2  2 |  * 96 |  2  {(ddee)}
-----------------------------+------------+----------+-------+---
oooo3oooo3oooo4oooo&#(c,d,e) | 1  3  3  1 |  3  6  3 |  3  3 | 64

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