Acronym ..., ico || spic
Name (degenerate) ico atop spic
Circumradius ∞   i.e. flat in euclidean space
Confer
general polytopal classes:
decomposition  

It either can be thought of as a degenerate 5D segmentotope with zero height, or as a 4D euclidean decomposition of the larger base into smaller bits.


Incidence matrix according to Dynkin symbol

ox3oo4oo3xx&#x   → height = 0
(ico || spic)

o.3o.4o.3o.    | 24   * |  8   6   0   0 | 12  12  24   0   0   0 |  6   8  24  24  0  0  0  0 | 1  1  8 12  6 0
.o3.o4.o3.o    |  * 144 |  0   1   4   4 |  0   4   4   4   8   4 |  0   4   8   4  1  4  4  1 | 0  1  4  4  1 1
---------------+--------+----------------+------------------------+----------------------------+----------------
.. .. .. x.    |  2   0 | 96   *   *   * |  3   0   3   0   0   0 |  3   0   3   6  0  0  0  0 | 1  0  1  3  3 0
oo3oo4oo3oo&#x |  1   1 |  * 144   *   * |  0   4   4   0   0   0 |  0   4   8   4  0  0  0  0 | 0  1  4  4  1 0
.x .. .. ..    |  0   2 |  *   * 288   * |  0   1   0   2   2   0 |  0   2   2   0  1  2  1  0 | 0  1  2  1  0 1
.. .. .. .x    |  0   2 |  *   *   * 288 |  0   0   1   0   2   2 |  0   0   2   2  0  1  2  1 | 0  0  1  2  1 1
---------------+--------+----------------+------------------------+----------------------------+----------------
.. .. o.3x.    |  3   0 |  3   0   0   0 | 96   *   *   *   *   * |  2   0   0   2  0  0  0  0 | 1  0  0  1  2 0
ox .. .. ..&#x |  1   2 |  0   2   1   0 |  * 288   *   *   *   * |  0   2   2   0  0  0  0  0 | 0  1  2  1  0 0
.. .. .. xx&#x |  2   2 |  1   2   0   1 |  *   * 288   *   *   * |  0   0   2   2  0  0  0  0 | 0  0  1  2  1 0
.x3.o .. ..    |  0   3 |  0   0   3   0 |  *   *   * 192   *   * |  0   1   0   0  1  1  0  0 | 0  1  1  0  0 1
.x .. .. .x    |  0   4 |  0   0   2   2 |  *   *   *   * 288   * |  0   0   1   0  0  1  1  0 | 0  0  1  1  0 1
.. .. .o3.x    |  0   3 |  0   0   0   3 |  *   *   *   *   * 192 |  0   0   0   1  0  0  1  1 | 0  0  0  1  1 1
---------------+--------+----------------+------------------------+----------------------------+----------------
.. o.4o.3x.      6   0 | 12   0   0   0 |  8   0   0   0   0   0 | 24   *   *   *  *  *  *  * | 1  0  0  0  1 0
ox3oo .. ..&#x   1   3 |  0   3   3   0 |  0   3   0   1   0   0 |  * 192   *   *  *  *  *  * | 0  1  1  0  0 0
ox .. .. xx&#x   2   4 |  1   4   2   2 |  0   2   2   0   1   0 |  *   * 288   *  *  *  *  * | 0  0  1  1  0 0
.. .. oo3xx&#x   3   3 |  3   3   0   3 |  1   0   3   0   0   1 |  *   *   * 192  *  *  *  * | 0  0  0  1  1 0
.x3.o4.o ..      0   6 |  0   0  12   0 |  0   0   0   8   0   0 |  *   *   *   * 24  *  *  * | 0  1  0  0  0 1
.x3.o .. .x      0   6 |  0   0   6   3 |  0   0   0   2   3   0 |  *   *   *   *  * 96  *  * | 0  0  1  0  0 1
.x .. .o3.x      0   6 |  0   0   3   6 |  0   0   0   0   3   2 |  *   *   *   *  *  * 96  * | 0  0  0  1  0 1
.. .o4.o3.x      0   6 |  0   0   0  12 |  0   0   0   0   0   8 |  *   *   *   *  *  *  * 24 | 0  0  0  0  1 1
---------------+--------+----------------+------------------------+----------------------------+----------------
o.3o.4o.3x.     24   0 | 96   0   0   0 | 96   0   0   0   0   0 | 24   0   0   0  0  0  0  0 | 1  *  *  *  * *
ox3oo4oo ..&#x   1   6 |  0   6  12   0 |  0  12   0   8   0   0 |  0   8   0   0  1  0  0  0 | * 24  *  *  * *
ox3oo .. xx&#x   2   6 |  1   6   6   3 |  0   6   3   2   3   0 |  0   2   3   0  0  1  0  0 | *  * 96  *  * *
ox .. oo3xx&#x   3   6 |  3   6   3   6 |  1   3   6   0   3   2 |  0   0   3   2  0  0  1  0 | *  *  * 96  * *
.. oo4oo3xx&#x   6   6 | 12   6   0  12 |  8   0  12   0   0   8 |  1   0   0   8  0  0  0  1 | *  *  *  * 24 *
.x3.o4.o3.x      0 144 |  0   0 288 288 |  0   0   0 192 288 192 |  0   0   0   0 24 96 96 24 | *  *  *  *  * 1

© 2004-2019
top of page