Acronym stidox
Name stellated dodecahedral hexacosachoron,
compound of 75 hex in ex army,
compound of 25 stico in ex army
Coxeter symbol 5{3,3,5}[75{3,3,4}]10{5,3,3}
Circumradius 1/sqrt(2) = 0.707107
Inradius 1/sqrt(8) = 0.353553
General of army ex
Colonel of regiment (is itself locally convex)
Admiral of fleet hi
Confer
compound-component:
hex  
general polytopal classes:
regular  

Comes in 2×2=4 types, depending on whether the vertices get identified (types A & C) or not (types B & D) and whether the components are considered as individual hexes (types A & B) or as 3-hex-compounds (sticoes, types C & D) in turn.


Incidence matrix

(Type A)

120 ♦   30 |   60 |   40 ||  5
----+------+------+------++---
  2 | 1800 |    4 |    4 ||  1
----+------+------+------++---
  3 |    3 | 2400 |    2 ||  1
----+------+------+------++---
♦ 4 |    6 |    4 | 1200 ||  1
----+------+------+------++---
♦ 8 |   24 |   32 |   16 || 75


(Type B)

600 ♦    6 |   12 |    8 ||  1
----+------+------+------++---
  2 | 1800 |    4 |    4 ||  1
----+------+------+------++---
  3 |    3 | 2400 |    2 ||  1
----+------+------+------++---
♦ 4 |    6 |    4 | 1200 ||  1
----+------+------+------++---
♦ 8 |   24 |   32 |   16 || 75


(Type C)

120 ♦   30 |   60 |   40 ||  5
----+------+------+------++---
  2 | 1800 |    4 |    4 ||  1
----+------+------+------++---
  3 |    3 | 2400 |    2 ||  1
----+------+------+------++---
♦ 4 |    6 |    4 | 1200 ||  1
----+------+------+------++---
♦24 |   72 |   96 |   48 || 25


(Type D)

600 ♦    6 |   12 |    8 ||  1
----+------+------+------++---
  2 | 1800 |    4 |    4 ||  1
----+------+------+------++---
  3 |    3 | 2400 |    2 ||  1
----+------+------+------++---
♦ 4 |    6 |    4 | 1200 ||  1
----+------+------+------++---
♦24 |   72 |   96 |   48 || 25

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