Acronym respic
Name rectified small prismated tetracontoctachoron
Circumradius sqrt[7+4 sqrt(2)] = 3.557647
Coordinates
  • (0, 1/sqrt(2), 1/sqrt(2), 2+sqrt(2))                & all permutations, all changes of sign
  • (1, (2+sqrt(2))/2, (2+sqrt(2))/2, 1+sqrt(2))   & all permutations, all changes of sign
  • (1/2, 1/2, (1+2 sqrt(2))/2, (3+2 sqrt(2))/2)   & all permutations, all changes of sign
  • (0, 1, 1+sqrt(2), 1+sqrt(2))                          & all permutations, all changes of sign
Confer
general polytopal classes:
isogonal  
External
links
polytopewiki  

Rectification wrt. a non-regular polytope is meant to be the singular instance of truncations on all vertices at such a depth that the hyperplane intersections on the former edges will coincide (provided such a choice exists). Within the specific case of spic all edges belong to a single orbit of symmetry, i.e. rectification clearly is applicable, without any recourse to Conway's ambification (chosing the former edge centers generally).

Still, because the pre-image uses different polygonal faces, this would result in 2 different edge sizes in the outcome polychoron. That one here is scaled such so that the shorter one becomes unity. Then the larger edge will have size q=sqrt(2).


Incidence matrix according to Dynkin symbol

uo3ox4xo3ou&#zq   → height = 0
                    u = 2 (pseudo)
(q-laced tegum sum of 2 inverted (u,x)-sricos)

o.3o.4o.3o.     | 288   * |   4    4   0 |   2   2   2   2   4   0   0 |  1  1  2   2  0
.o3.o4.o3.o     |   * 288 |   0    4   4 |   0   0   2   4   2   2   2 |  0  2  1   2  1
----------------+---------+--------------+-----------------------------+----------------
.. .. x. ..     |   2   0 | 576    *   * |   1   1   0   0   1   0   0 |  1  0  1   1  0
oo3oo4oo3oo&#q  |   1   1 |   * 1152   * |   0   0   1   1   1   0   0 |  0  1  1   1  0
.. .x .. ..     |   0   2 |   *    * 576 |   0   0   0   1   0   1   1 |  0  1  0   1  1
----------------+---------+--------------+-----------------------------+----------------
.. o.4x. ..     |   4   0 |   4    0   0 | 144   *   *   *   *   *   * |  1  0  0   1  0  x-{4}
.. .. x.3o.     |   3   0 |   3    0   0 |   * 192   *   *   *   *   * |  1  0  1   0  0  x-{3}
uo .. .. ou&#zq |   2   2 |   0    4   0 |   *   * 288   *   *   *   * |  0  1  1   0  0  q-{4}
.. ox .. ..&#q  |   1   2 |   0    2   1 |   *   *   * 576   *   *   * |  0  1  0   1  0  xqq
.. .. xo ..&#q  |   2   1 |   1    2   0 |   *   *   *   * 576   *   * |  0  0  1   1  0  xqq
.o3.x .. ..     |   0   3 |   0    0   3 |   *   *   *   *   * 192   * |  0  1  0   0  1  x-{3}
.. .x4.o ..     |   0   4 |   0    0   4 |   *   *   *   *   *   * 144 |  0  0  0   1  1  x-{3}
----------------+---------+--------------+-----------------------------+----------------
.. o.4x.3o.     |  12   0 |  24    0   0 |   6   8   0   0   0   0   0 | 24  *  *   *  *  co
uo3ox .. ou&#zq |   3   6 |   0   12   6 |   0   0   3   6   0   2   0 |  * 96  *   *  *  retrip
uo .. xo3ou&#zq |   6   3 |   6   12   0 |   0   2   3   0   6   0   0 |  *  * 96   *  *  retrip
.. ox4xo ..&#q  |   4   4 |   4    8   4 |   1   0   0   4   4   0   1 |  *  *  * 144  *  tall (x,q)-4ap
.o3.x4.o ..     |   0  12 |   0    0  24 |   0   0   0   0   0   8   6 |  *  *  *   * 24  co
or
o.3o.4o.3o.     & | 576 |    4    4 |   2   2   2    6 |  1   3   2
------------------+-----+-----------+------------------+-----------
.. .. x. ..     & |   2 | 1152    * |   1   1   0    1 |  1   1   1
oo3oo3oo3oo&#q    |   2 |    * 1152 |   0   0   1    2 |  0   2   1
------------------+-----+-----------+------------------+-----------
.. o.4x. ..     & |   4 |    4    0 | 288   *   *    * |  1   0   1
.. .. x.3o.     & |   3 |    3    0 |   * 384   *    * |  1   1   0
uo .. .. ou&#zq   |   4 |    0    4 |   *   * 288    * |  0   2   0
.. ox .. ..&#q  & |   3 |    1    2 |   *   *   * 1152 |  0   1   1
------------------+-----+-----------+------------------+-----------
.. o.4x.3o.     & |  12 |   24    0 |   6   8   0    0 | 48   *   *  co
uo3ox .. ou&#zq & |   9 |    6   12 |   0   2   3    6 |  * 192   *  retrip
.. ox4xo ..&#q    |   8 |    8    8 |   2   0   0    8 |  *   * 144  tall (x,q)-4ap

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