Acronym ..., deca || gippid
Name (degenerate) deca atop gippid
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

ox3xx3xx3ox&#x   → height = 0
(deca || gippid)

o.3o.3o.3o.    | 30   * |  2  2   4  0  0  0  0 |  1  4  1  2  4  4  2  0  0  0  0  0  0 | 2 2  2  2  1  4  2  2 0  0  0 0 | 1 2  1  1 2 0
.o3.o3.o3.o    |  * 120 |  0  0   1  1  1  1  1 |  0  0  0  1  1  1  1  1  1  1  1  1  1 | 0 0  1  1  1  1  1  1 1  1  1 1 | 0 1  1  1 1 1
---------------+--------+-----------------------+----------------------------------------+---------------------------------+--------------
.. x. .. ..    |  2   0 | 30  *   *  *  *  *  * |  1  2  0  0  2  0  0  0  0  0  0  0  0 | 2 1  2  0  0  2  1  0 0  0  0 0 | 1 2  1  0 1 0
.. .. x. ..    |  2   0 |  * 30   *  *  *  *  * |  0  2  1  0  0  2  0  0  0  0  0  0  0 | 1 2  0  1  0  2  0  2 0  0  0 0 | 1 1  0  1 2 0
oo3oo3oo3oo&#x |  1   1 |  *  * 120  *  *  *  * |  0  0  0  1  1  1  1  0  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 |  *  *   * 60  *  *  * |  0  0  0  1  0  0  0  1  1  1  0  0  0 | 0 0  1  1  1  0  0  0 1  1  1 0 | 0 1  1  1 0 1
.. .x .. ..    |  0   2 |  *  *   *  * 60  *  * |  0  0  0  0  1  0  0  1  0  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 |  *  *   *  *  * 60  * |  0  0  0  0  0  1  0  0  1  0  1  0  1 | 0 0  0  1  0  1  0  1 1  0  1 1 | 0 1  0  1 1 1
.. .. .. .x    |  0   2 |  *  *   *  *  *  * 60 |  0  0  0  0  0  0  1  0  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  0 | 10  *  *  *  *  *  *  *  *  *  *  *  * | 2 0  2  0  0  0  0  0 0  0  0 0 | 1 2  1  0 0 0
.. x.3x. ..    |  6   0 |  3  3   0  0  0  0  0 |  * 20  *  *  *  *  *  *  *  *  *  *  * | 1 1  0  0  0  1  0  0 0  0  0 0 | 1 1  0  0 1 0
.. .. x.3o.    |  3   0 |  0  3   0  0  0  0  0 |  *  * 10  *  *  *  *  *  *  *  *  *  * | 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  0 |  *  *  * 60  *  *  *  *  *  *  *  *  * | 0 0  1  1  1  0  0  0 0  0  0 0 | 0 1  1  1 0 0
.. xx .. ..&#x |  2   2 |  1  0   2  0  1  0  0 |  *  *  *  * 60  *  *  *  *  *  *  *  * | 0 0  1  0  0  1  1  0 0  0  0 0 | 0 1  1  0 1 0
.. .. xx ..&#x |  2   2 |  0  1   2  0  0  1  0 |  *  *  *  *  * 60  *  *  *  *  *  *  * | 0 0  0  1  0  1  0  1 0  0  0 0 | 0 1  0  1 1 0
.. .. .. ox&#x |  1   2 |  0  0   2  0  0  0  1 |  *  *  *  *  *  * 60  *  *  *  *  *  * | 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  0 |  *  *  *  *  *  *  * 20  *  *  *  *  * | 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  0 |  *  *  *  *  *  *  *  * 30  *  *  *  * | 0 0  0  1  0  0  0  0 1  0  1 0 | 0 1  0  1 0 1
.x .. .. .x    |  0   4 |  0  0   0  2  0  0  2 |  *  *  *  *  *  *  *  *  * 30  *  *  * | 0 0  0  0  1  0  0  0 0  1  1 0 | 0 0  1  1 0 1
.. .x3.x ..    |  0   6 |  0  0   0  0  3  3  0 |  *  *  *  *  *  *  *  *  *  * 20  *  * | 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  0  2 |  *  *  *  *  *  *  *  *  *  *  * 30  * | 0 0  0  0  0  0  1  0 0  1  0 1 | 0 0  1  0 1 1
.. .. .x3.x    |  0   6 |  0  0   0  0  0  3  3 |  *  *  *  *  *  *  *  *  *  *  *  * 20 | 0 0  0  0  0  0  0  1 0  0  1 1 | 0 0  0  1 1 1
---------------+--------+-----------------------+----------------------------------------+---------------------------------+--------------
o.3x.3x. ..     12   0 | 12  6   0  0  0  0  0 |  4  4  0  0  0  0  0  0  0  0  0  0  0 | 5 *  *  *  *  *  *  * *  *  * * | 1 1  0  0 0 0
.. x.3x.3o.     12   0 |  6 12   0  0  0  0  0 |  0  4  4  0  0  0  0  0  0  0  0  0  0 | * 5  *  *  *  *  *  * *  *  * * | 1 0  0  0 1 0
ox3xx .. ..&#x   3   6 |  3  0   6  3  3  0  0 |  1  0  0  3  3  0  0  1  0  0  0  0  0 | * * 20  *  *  *  *  * *  *  * * | 0 1  1  0 0 0
ox .. xx ..&#x   2   4 |  0  1   4  2  0  2  0 |  0  0  0  2  0  2  0  0  1  0  0  0  0 | * *  * 30  *  *  *  * *  *  * * | 0 1  0  1 0 0
ox .. .. ox&#x   1   4 |  0  0   4  2  0  0  2 |  0  0  0  2  0  0  2  0  0  1  0  0  0 | * *  *  * 30  *  *  * *  *  * * | 0 0  1  1 0 0
.. xx3xx ..&#x   6   6 |  3  3   6  0  3  3  0 |  0  1  0  0  3  3  0  0  0  0  1  0  0 | * *  *  *  * 20  *  * *  *  * * | 0 1  0  0 1 0
.. xx .. ox&#x   2   4 |  1  0   4  0  2  0  2 |  0  0  0  0  2  0  2  0  0  0  0  1  0 | * *  *  *  *  * 30  * *  *  * * | 0 0  1  0 1 0
.. .. xx3ox&#x   3   6 |  0  3   6  0  0  3  3 |  0  0  1  0  0  3  3  0  0  0  0  0  1 | * *  *  *  *  *  * 20 *  *  * * | 0 0  0  1 1 0
.x3.x3.x ..      0  24 |  0  0   0 12 12 12  0 |  0  0  0  0  0  0  0  4  6  0  4  0  0 | * *  *  *  *  *  *  * 5  *  * * | 0 1  0  0 0 1
.x3.x .. .x      0  12 |  0  0   0  6  6  0  6 |  0  0  0  0  0  0  0  2  0  3  0  3  0 | * *  *  *  *  *  *  * * 10  * * | 0 0  1  0 0 1
.x .. .x3.x      0  12 |  0  0   0  6  0  6  6 |  0  0  0  0  0  0  0  0  3  3  0  0  2 | * *  *  *  *  *  *  * *  * 10 * | 0 0  0  1 0 1
.. .x3.x3.x      0  24 |  0  0   0  0 12 12 12 |  0  0  0  0  0  0  0  0  0  0  4  6  4 | * *  *  *  *  *  *  * *  *  * 5 | 0 0  0  0 1 1
---------------+--------+-----------------------+----------------------------------------+---------------------------------+--------------
o.3x.3x.3o.     30   0 | 30 30   0  0  0  0  0 | 10 20 10  0  0  0  0  0  0  0  0  0  0 | 5 5  0  0  0  0  0  0 0  0  0 0 | 1 *  *  * * *
ox3xx3xx ..&#x  12  24 | 12  6  24 12 12 12  0 |  4  4  0 12 12 12  0  4  6  0  4  0  0 | 1 0  4  6  0  4  0  0 1  0  0 0 | * 5  *  * * *
ox3xx .. ox&#x   3  12 |  3  0  12  6  6  0  6 |  1  0  0  6  6  0  6  2  0  3  0  3  0 | 0 0  2  0  3  0  3  0 0  1  0 0 | * * 10  * * *
ox .. xx3ox&#x   3  12 |  0  3  12  6  0  6  6 |  0  0  1  6  0  6  6  0  3  3  0  0  2 | 0 0  0  3  3  0  0  2 0  0  1 0 | * *  * 10 * *
.. xx3xx3ox&#x  12  24 |  6 12  24  0 12 12 12 |  0  4  4  0 12 12 12  0  0  0  4  6  4 | 0 1  0  0  0  4  6  4 0  0  0 1 | * *  *  * 5 *
.x3.x3.x3.x      0 120 |  0  0   0 60 60 60 60 |  0  0  0  0  0  0  0 20 30 30 20 30 20 | 0 0  0  0  0  0  0  0 5 10 10 5 | * *  *  * * 1
or
o.3o.3o.3o.      | 30   * |  4   4   0   0 |  2  4   4   8  0  0  0  0 |  4  4  4  1  4  0  0 | 1  4  2 0
.o3.o3.o3.o      |  * 120 |  0   1   2   2 |  0  0   2   2  2  2  1  1 |  0  2  2  1  1  2  2 | 0  2  2 1
-----------------+--------+----------------+---------------------------+----------------------+----------
.. x. .. ..    & |  2   0 | 60   *   *   * |  1  2   0   2  0  0  0  0 |  3  2  1  0  2  0  0 | 1  3  1 0
oo3oo3oo3oo&#x   |  1   1 |  * 120   *   * |  0  0   2   2  0  0  0  0 |  0  2  2  1  1  0  0 | 0  2  2 0
.x .. .. ..    & |  0   2 |  *   * 120   * |  0  0   1   0  1  1  1  0 |  0  1  1  1  0  1  2 | 0  1  2 1
.. .x .. ..    & |  0   2 |  *   *   * 120 |  0  0   0   1  1  1  0  1 |  0  1  1  0  1  2  1 | 0  2  1 1
-----------------+--------+----------------+---------------------------+----------------------+----------
o.3x. .. ..    & |  3   0 |  3   0   0   0 | 20  *   *   *  *  *  *  * |  2  2  0  0  0  0  0 | 1  2  1 0
.. x.3x. ..      |  6   0 |  6   0   0   0 |  * 20   *   *  *  *  *  * |  2  0  0  0  1  0  0 | 1  2  0 0
ox .. .. ..&#x & |  1   2 |  0   2   1   0 |  *  * 120   *  *  *  *  * |  0  1  1  1  0  0  0 | 0  1  2 0
.. xx .. ..&#x & |  2   2 |  1   2   0   1 |  *  *   * 120  *  *  *  * |  0  1  1  0  1  0  0 | 0  2  1 0
.x3.x .. ..    & |  0   6 |  0   0   3   3 |  *  *   *   * 40  *  *  * |  0  1  0  0  0  1  1 | 0  1  1 1
.x .. .x ..    & |  0   4 |  0   0   2   2 |  *  *   *   *  * 60  *  * |  0  0  1  0  0  1  1 | 0  1  1 1
.x .. .. .x      |  0   4 |  0   0   4   0 |  *  *   *   *  *  * 30  * |  0  0  0  1  0  0  2 | 0  0  2 1
.. .x3.x ..      |  0   6 |  0   0   0   6 |  *  *   *   *  *  *  * 20 |  0  0  0  0  1  2  0 | 0  2  0 1
-----------------+--------+----------------+---------------------------+----------------------+----------
o.3x.3x. ..    &  12   0 | 18   0   0   0 |  4  4   0   0  0  0  0  0 | 10  *  *  *  *  *  * | 1  1  0 0
ox3xx .. ..&#x &   3   6 |  3   6   3   3 |  1  0   3   3  1  0  0  0 |  * 40  *  *  *  *  * | 0  1  1 0
ox .. xx ..&#x &   2   4 |  1   4   2   2 |  0  0   2   2  0  1  0  0 |  *  * 60  *  *  *  * | 0  1  1 0
ox .. .. ox&#x     1   4 |  0   4   4   0 |  0  0   4   0  0  0  1  0 |  *  *  * 30  *  *  * | 0  0  2 0
.. xx3xx ..&#x     6   6 |  6   6   0   6 |  0  1   0   6  0  0  0  1 |  *  *  *  * 20  *  * | 0  2  0 0
.x3.x3.x ..    &   0  24 |  0   0  12  24 |  0  0   0   0  4  6  0  4 |  *  *  *  *  * 10  * | 0  1  0 1
.x3.x .. .x    &   0  12 |  0   0  12   6 |  0  0   0   0  2  3  3  0 |  *  *  *  *  *  * 20 | 0  0  1 1
-----------------+--------+----------------+---------------------------+----------------------+----------
o.3x.3x.3o.       30   0 | 60   0   0   0 | 20 20   0   0  0  0  0  0 | 10  0  0  0  0  0  0 | 1  *  * *
ox3xx3xx ..&#x &  12  24 | 18  24  12  24 |  4  4  12  24  4  6  0  4 |  1  4  6  0  4  1  0 | * 10  * *
ox3xx .. ox&#x &   3  12 |  3  12  12   6 |  1  0  12   6  2  3  3  0 |  0  2  3  3  0  0  1 | *  * 20 *
.x3.x3.x3.x        0 120 |  0   0 120 120 |  0  0   0   0 40 60 30 20 |  0  0  0  0  0 10 20 | *  *  * 1

© 2004-2019
top of page