Acronym ..., tat || prit
Name (degenerate) tat atop prit
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

ox3ox3xo4xx&#x   → height = 0
(tat || prit)

o.3o.3o.4o.    | 64   * |  3  1   6  0   0   0 |  3  3   3   3   6   6  0  0  0  0  0 |  1 3  1  3  3  3  3  6  0  0  0 0 | 1  1  1  3 3 0
.o3.o3.o4.o    |  * 192 |  0  0   2  1   2   2 |  0  0   2   2   1   2  2  2  1  2  1 |  0 0  2  1  2  1  2  1  1  2  1 1 | 0  1  2  1 1 1
---------------+--------+----------------------+--------------------------------------+-----------------------------------+---------------
.. .. x. ..    |  2   0 | 96  *   *  *   *   * |  2  1   0   0   2   0  0  0  0  0  0 |  1 2  0  1  0  2  0  2  0  0  0 0 | 1  1  0  1 2 0
.. .. .. x.    |  2   0 |  * 32   *  *   *   * |  0  3   0   0   0   6  0  0  0  0  0 |  0 3  0  0  3  0  3  6  0  0  0 0 | 1  0  1  3 3 0
oo3oo3oo4oo&#x |  1   1 |  *  * 384  *   *   * |  0  0   1   1   1   1  0  0  0  0  0 |  0 0  1  1  1  1  1  1  0  0  0 0 | 0  1  1  1 1 0
.x .. .. ..    |  0   2 |  *  *   * 96   *   * |  0  0   2   0   0   0  2  2  0  0  0 |  0 0  2  1  2  0  0  0  1  2  1 0 | 0  1  2  1 0 1
.. .x .. ..    |  0   2 |  *  *   *  * 192   * |  0  0   0   1   0   0  1  0  1  1  0 |  0 0  1  0  0  1  1  0  1  1  0 1 | 0  1  1  0 1 1
.. .. .. .x    |  0   2 |  *  *   *  *   * 192 |  0  0   0   0   0   1  0  1  0  1  1 |  0 0  0  0  1  0  1  1  0  1  1 1 | 0  0  1  1 1 1
---------------+--------+----------------------+--------------------------------------+-----------------------------------+---------------
.. o.3x. ..    |  3   0 |  3  0   0  0   0   0 | 64  *   *   *   *   *  *  *  *  *  * |  1 1  0  0  0  1  0  0  0  0  0 0 | 1  1  0  0 1 0
.. .. x.4x.    |  8   0 |  4  4   0  0   0   0 |  * 24   *   *   *   *  *  *  *  *  * |  0 2  0  0  0  0  0  2  0  0  0 0 | 1  0  0  1 2 0
ox .. .. ..&#x |  1   2 |  0  0   2  1   0   0 |  *  * 192   *   *   *  *  *  *  *  * |  0 0  1  1  1  0  0  0  0  0  0 0 | 0  1  1  1 0 0
.. ox .. ..&#x |  1   2 |  0  0   2  0   1   0 |  *  *   * 192   *   *  *  *  *  *  * |  0 0  1  0  0  1  1  0  0  0  0 0 | 0  1  1  0 1 0
.. .. xo ..&#x |  2   1 |  1  0   2  0   0   0 |  *  *   *   * 192   *  *  *  *  *  * |  0 0  0  1  0  1  0  1  0  0  0 0 | 0  1  0  1 1 0
.. .. .. xx&#x |  2   2 |  0  1   2  0   0   1 |  *  *   *   *   * 192  *  *  *  *  * |  0 0  0  0  1  0  1  1  0  0  0 0 | 0  0  1  1 1 0
.x3.x .. ..    |  0   6 |  0  0   0  3   3   0 |  *  *   *   *   *   * 64  *  *  *  * |  0 0  1  0  0  0  0  0  1  1  0 0 | 0  1  1  0 0 1
.x .. .. .x    |  0   4 |  0  0   0  2   0   2 |  *  *   *   *   *   *  * 96  *  *  * |  0 0  0  0  1  0  0  0  0  1  1 0 | 0  0  1  1 0 1
.. .x3.o ..    |  0   3 |  0  0   0  0   3   0 |  *  *   *   *   *   *  *  * 64  *  * |  0 0  0  0  0  1  0  0  1  0  0 1 | 0  1  0  0 1 1
.. .x .. .x    |  0   4 |  0  0   0  0   2   2 |  *  *   *   *   *   *  *  *  * 96  * |  0 0  0  0  0  0  1  0  0  1  0 1 | 0  0  1  0 1 1
.. .. .o4.x    |  0   4 |  0  0   0  0   0   4 |  *  *   *   *   *   *  *  *  *  * 48 |  0 0  0  0  0  0  0  1  0  0  1 1 | 0  0  0  1 1 1
---------------+--------+----------------------+--------------------------------------+-----------------------------------+---------------
o.3o.3x. ..      4   0 |  6  0   0  0   0   0 |  4  0   0   0   0   0  0  0  0  0  0 | 16 *  *  *  *  *  *  *  *  *  * * | 1  1  0  0 0 0
.. o.3x.4x.     24   0 | 24 12   0  0   0   0 |  8  6   0   0   0   0  0  0  0  0  0 |  * 8  *  *  *  *  *  *  *  *  * * | 1  0  0  0 1 0
ox3ox .. ..&#x   1   6 |  0  0   6  3   3   0 |  0  0   3   3   0   0  1  0  0  0  0 |  * * 64  *  *  *  *  *  *  *  * * | 0  1  1  0 0 0
ox .. xo ..&#x   2   2 |  1  0   4  1   0   0 |  0  0   2   0   2   0  0  0  0  0  0 |  * *  * 96  *  *  *  *  *  *  * * | 0  1  0  1 0 0
ox .. .. xx&#x   2   4 |  0  1   4  2   0   2 |  0  0   2   0   0   2  0  1  0  0  0 |  * *  *  * 96  *  *  *  *  *  * * | 0  0  1  1 0 0
.. ox3xo ..&#x   3   3 |  3  0   6  0   3   0 |  1  0   0   3   3   0  0  0  1  0  0 |  * *  *  *  * 64  *  *  *  *  * * | 0  1  0  0 1 0
.. ox .. xx&#x   2   4 |  0  1   4  0   2   2 |  0  0   0   2   0   2  0  0  0  1  0 |  * *  *  *  *  * 96  *  *  *  * * | 0  0  1  0 1 0
.. .. xo4xx&#x   8   4 |  4  4   8  0   0   4 |  0  1   0   0   4   4  0  0  0  0  1 |  * *  *  *  *  *  * 48  *  *  * * | 0  0  0  1 1 0
.x3.x3.o ..      0  12 |  0  0   0  6  12   0 |  0  0   0   0   0   0  4  0  4  0  0 |  * *  *  *  *  *  *  * 16  *  * * | 0  1  0  0 0 1
.x3.x .. .x      0  12 |  0  0   0  6   6   6 |  0  0   0   0   0   0  2  3  0  3  0 |  * *  *  *  *  *  *  *  * 32  * * | 0  0  1  0 0 1
.x .. .o4.x      0   8 |  0  0   0  4   0   8 |  0  0   0   0   0   0  0  4  0  0  2 |  * *  *  *  *  *  *  *  *  * 24 * | 0  0  0  1 0 1
.. .x3.o4.x      0  24 |  0  0   0  0  24  24 |  0  0   0   0   0   0  0  0  8 12  6 |  * *  *  *  *  *  *  *  *  *  * 8 | 0  0  0  0 1 1
---------------+--------+----------------------+--------------------------------------+-----------------------------------+---------------
o.3o.3x.4x.     64   0 | 96 32   0  0   0   0 | 64 24   0   0   0   0  0  0  0  0  0 | 16 8  0  0  0  0  0  0  0  0  0 0 | 1  *  *  * * *
ox3ox3xo ..&#x   4  12 |  6  0  24  6  12   0 |  4  0  12  12  12   0  4  0  4  0  0 |  1 0  4  6  0  4  0  0  1  0  0 0 | * 16  *  * * *
ox3ox .. xx&#x   2  12 |  0  1  12  6   6   6 |  0  0   6   6   0   6  2  3  0  3  0 |  0 0  2  0  3  0  3  0  0  1  0 0 | *  * 32  * * *
ox .. xo4xx&#x   8   8 |  4  4  16  4   0   8 |  0  1   8   0   8   8  0  4  0  0  2 |  0 0  0  4  4  0  0  2  0  0  1 0 | *  *  * 24 * *
.. ox3xo4xx&#x  24  24 | 24 12  48  0  24  24 |  8  6   0  24  24  24  0  0  8 12  6 |  0 1  0  0  0  8 12  6  0  0  0 1 | *  *  *  * 8 *
.x3.x3.o4.x      0 192 |  0  0   0 96 192 192 |  0  0   0   0   0   0 64 96 64 96 48 |  0 0  0  0  0  0  0  0 16 32 24 8 | *  *  *  * * 1

© 2004-2020
top of page