Acronym ...
Name q3o4o3x,
variant of spic
Circumradius sqrt(5) = 2.236068
Coordinates
  • (2, 2, 1, 1)/sqrt(2)       & all permutations, all changes of sign
    (vertex inscribed (x,q)-srit)
  • (3, 1, 0, 0)/sqrt(2)       & all permutations, all changes of sign
    (vertex inscribed (u,x)-thex)
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at (x,q)-{4} between q x3o and x q3o:   arccos[-sqrt(8)/3] = 160.528779°
  • at q-{3} between q-oct and x q3o:   150°
  • at x-{3} between x-oct and q x3o:   150°
Face vector 144, 576, 672, 240
Confer
uniform relative:
spic   srit   thex  

Incidence matrix according to Dynkin symbol

q3o4o3x

. . . . | 144 |   4   4 |   4   8   4 |  1  4  4  1
--------+-----+---------+-------------+------------
q . . . |   2 | 288   * |   2   2   0 |  1  2  1  0  q
. . . x |   2 |   * 288 |   0   2   2 |  0  1  2  1  x
--------+-----+---------+-------------+------------
q3o . . |   3 |   3   0 | 192   *   * |  1  1  0  0
q . . x |   4 |   2   2 |   * 288   * |  0  1  1  0
. . o3x |   3 |   0   3 |   *   * 192 |  0  0  1  1
--------+-----+---------+-------------+------------
q3o4o . ♦   6 |  12   0 |   8   0   0 | 24  *  *  *
q3o . x ♦   6 |   6   3 |   2   3   0 |  * 96  *  *
q . o3x ♦   6 |   3   6 |   0   3   2 |  *  * 96  *
. o4o3x ♦   6 |   0  12 |   0   0   8 |  *  *  * 24


((ou3xx3oo4qo))&#zq   → height = 0
                        where u = 2 (pseudo)

  o.3o.3o.4o.       | 96  * |   4  2   2  0 |  2  2  4   4   4  0 |  1  2  1  2  4 0
  .o3.o3.o4.o       |  * 48 |   0  0   4  4 |  0  0  0   8   4  4 |  0  0  1  4  4 1
--------------------+-------+---------------+---------------------+-----------------
  .. x. .. ..       |  2  0 | 192  *   *  * |  1  1  1   1   0  0 |  1  1  0  1  1 0  x
  .. .. .. q.       |  2  0 |   * 96   *  * |  0  0  2   0   2  0 |  0  1  1  0  2 0  q
  oo3oo3oo4oo  &#q  |  1  1 |   *  * 192  * |  0  0  0   2   2  0 |  0  0  1  1  2 0  q
  .. .x .. ..       |  0  2 |   *  *   * 96 |  0  0  0   2   0  2 |  0  0  0  2  1 1  x
--------------------+-------+---------------+---------------------+-----------------
  o.3x. .. ..       |  3  0 |   3  0   0  0 | 64  *  *   *   *  * |  1  1  0  0  0 0
  .. x.3o. ..       |  3  0 |   3  0   0  0 |  * 64  *   *   *  * |  1  0  0  1  0 0
  .. x. .. q.       |  4  0 |   2  2   0  0 |  *  * 96   *   *  * |  0  1  0  0  1 0
  .. xx .. ..  &#q  |  2  2 |   1  0   2  1 |  *  *  * 192   *  * |  0  0  0  1  1 0
  .. .. .. qo  &#q  |  2  1 |   0  1   2  0 |  *  *  *   * 192  * |  0  0  1  0  1 0
  .. .x3.o ..       |  0  3 |   0  0   0  3 |  *  *  *   *   * 64 |  0  0  0  1  0 1
--------------------+-------+---------------+---------------------+-----------------
  o.3x.3o. ..       ♦  6  0 |  12  0   0  0 |  4  4  0   0   0  0 | 16  *  *  *  * *
  o.3x. .. q.       ♦  6  0 |   6  3   0  0 |  2  0  3   0   0  0 |  * 32  *  *  * *
((ou .. oo4qo))&#zq ♦  4  2 |   0  4   8  0 |  0  0  0   0   8  0 |  *  * 24  *  * *
  .. xx3oo ..  &#q  ♦  3  3 |   3  0   3  3 |  0  1  0   3   0  1 |  *  *  * 64  * *
  .. xx .. qo  &#q  ♦  4  2 |   2  2   4  1 |  0  0  1   2   2  0 |  *  *  *  * 96 *
  .. .x3.o4.o       ♦  0  6 |   0  0   0 12 |  0  0  0   0   0  8 |  *  *  *  *  * 8

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