Acronym trisqdip
Name trisquare duoprism,
compound of 9 tes in twaddip army
Coxeter symbol {12}x{12}[9{4,3,3}]
Circumradius 1
Pattern
a---b---c---a---b---c---a---b---c---a---b---c---
|   |   |   |   |   |   |   |   |   |   |   |
d---e---f---d---e---f---d---e---f---d---e---f---
|   |   |   |   |   |   |   |   |   |   |   |
g---h---i---g---h---i---g---h---i---g---h---i---
|   |   |   |   |   |   |   |   |   |   |   |
a---b---c---a---b---c---a---b---c---a---b---c---
|   |   |   |   |   |   |   |   |   |   |   |
d---e---f---d---e---f---d---e---f---d---e---f---
|   |   |   |   |   |   |   |   |   |   |   |
g---h---i---g---h---i---g---h---i---g---h---i---
|   |   |   |   |   |   |   |   |   |   |   |
a---b---c---a---b---c---a---b---c---a---b---c---
|   |   |   |   |   |   |   |   |   |   |   |
d---e---f---d---e---f---d---e---f---d---e---f---
|   |   |   |   |   |   |   |   |   |   |   |
g---h---i---g---h---i---g---h---i---g---h---i---
|   |   |   |   |   |   |   |   |   |   |   |
a---b---c---a---b---c---a---b---c---a---b---c---
|   |   |   |   |   |   |   |   |   |   |   |
d---e---f---d---e---f---d---e---f---d---e---f---
|   |   |   |   |   |   |   |   |   |   |   |
g---h---i---g---h---i---g---h---i---g---h---i---
|   |   |   |   |   |   |   |   |   |   |   |

Comes in 2 types, depending on the triples of coplanar squares: being counted separately (type A) or being combined to compounds (trisqs) as well (type B).


Incidence matrix according to Dynkin symbol

(Type A: no identifications)

144 |   4 |   4  2 |  4 || 1
----+-----+--------+----++--
  2 | 288 |   2  1 |  3 || 1
----+-----+--------+----++--
  4 |   4 | 144  * |  2 || 1  within pattern plane
  4 |   4 |   * 72 |  2 || 1  orthogonal to pattern plane
----+-----+--------+----++--
  8 |  12 |   4  2 | 72 || 1  cube
----+-----+--------+----++--
 16 |  32 |  16  8 |  8 || 9  tes

(Type B: compounded squares)

144 |   4 |   4  2 |  4 || 1
----+-----+--------+----++--
  2 | 288 |   2  1 |  3 || 1
----+-----+--------+----++--
  4 |   4 | 144  * |  2 || 1  within pattern plane
 12 |  12 |   * 24 |  2 || 3  trisq (3{4}-comp.)
----+-----+--------+----++--
 24 |  36 |  12  2 | 24 || 3  (3{4}-comp.)-prism
----+-----+--------+----++--
 16 |  32 |  16  8 |  8 || 9  tes

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