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

xo3ox3ox3xo&#x   → height = 0
(spid || deca)

o.3o.3o.3o.    | 20  * |  3  3   6  0  0 |  3  6  3  6  3  3  6  0  0  0 | 1  3  3 1  3  3  6  1  3  3 0 0 | 1 1  3  3 1 0
.o3.o3.o3.o    |  * 30 |  0  0   4  2  2 |  0  0  0  2  4  4  2  1  4  1 | 0  0  0 0  2  2  1  4  2  2 2 2 | 0 2  1  1 2 1
---------------+-------+-----------------+-------------------------------+---------------------------------+--------------
x. .. .. ..    |  2  0 | 30  *   *  *  * |  2  2  0  2  0  0  0  0  0  0 | 1  2  1 0  2  1  2  0  0  0 0 0 | 1 1  2  1 0 0
.. .. .. x.    |  2  0 |  * 30   *  *  * |  0  2  2  0  0  0  2  0  0  0 | 0  1  2 1  0  0  2  0  1  2 0 0 | 1 0  1  2 1 0
oo3oo3oo3oo&#x |  1  1 |  *  * 120  *  * |  0  0  0  1  1  1  1  0  0  0 | 0  0  0 0  1  1  1  1  1  1 0 0 | 0 1  1  1 1 0
.. .x .. ..    |  0  2 |  *  *   * 30  * |  0  0  0  0  2  0  0  1  2  0 | 0  0  0 0  2  0  0  2  1  0 2 1 | 0 2  1  0 1 1
.. .. .x ..    |  0  2 |  *  *   *  * 30 |  0  0  0  0  0  2  0  0  2  1 | 0  0  0 0  0  1  0  2  0  2 1 2 | 0 1  0  1 2 1
---------------+-------+-----------------+-------------------------------+---------------------------------+--------------
x.3o. .. ..    |  3  0 |  3  0   0  0  0 | 20  *  *  *  *  *  *  *  *  * | 1  1  0 0  1  0  0  0  0  0 0 0 | 1 1  1  0 0 0
x. .. .. x.    |  4  0 |  2  2   0  0  0 |  * 30  *  *  *  *  *  *  *  * | 0  1  1 0  0  0  1  0  0  0 0 0 | 1 0  1  1 0 0
.. .. o.3x.    |  3  0 |  0  3   0  0  0 |  *  * 20  *  *  *  *  *  *  * | 0  0  1 1  0  0  0  0  0  1 0 0 | 1 0  0  1 1 0
xo .. .. ..&#x |  2  1 |  1  0   2  0  0 |  *  *  * 60  *  *  *  *  *  * | 0  0  0 0  1  1  1  0  0  0 0 0 | 0 1  1  1 0 0
.. ox .. ..&#x |  1  2 |  0  0   2  1  0 |  *  *  *  * 60  *  *  *  *  * | 0  0  0 0  1  0  0  1  1  0 0 0 | 0 1  1  0 1 0
.. .. ox ..&#x |  1  2 |  0  0   2  0  1 |  *  *  *  *  * 60  *  *  *  * | 0  0  0 0  0  1  0  1  0  1 0 0 | 0 1  0  1 1 0
.. .. .. xo&#x |  2  1 |  0  1   2  0  0 |  *  *  *  *  *  * 60  *  *  * | 0  0  0 0  0  0  1  0  1  1 0 0 | 0 0  1  1 1 0
.o3.x .. ..    |  0  3 |  0  0   0  3  0 |  *  *  *  *  *  *  * 10  *  * | 0  0  0 0  2  0  0  0  0  0 2 0 | 0 2  1  0 0 1
.. .x3.x ..    |  0  6 |  0  0   0  3  3 |  *  *  *  *  *  *  *  * 20  * | 0  0  0 0  0  0  0  1  0  0 1 1 | 0 1  0  0 1 1
.. .. .x3.o    |  0  3 |  0  0   0  0  3 |  *  *  *  *  *  *  *  *  * 10 | 0  0  0 0  0  0  0  0  0  2 0 2 | 0 0  0  1 2 1
---------------+-------+-----------------+-------------------------------+---------------------------------+--------------
x.3o.3o. ..      4  0 |  6  0   0  0  0 |  4  0  0  0  0  0  0  0  0  0 | 5  *  * *  *  *  *  *  *  * * * | 1 1  0  0 0 0
x.3o. .. x.      6  0 |  6  3   0  0  0 |  2  3  0  0  0  0  0  0  0  0 | * 10  * *  *  *  *  *  *  * * * | 1 0  1  0 0 0
x. .. o.3x.      6  0 |  3  6   0  0  0 |  0  3  2  0  0  0  0  0  0  0 | *  * 10 *  *  *  *  *  *  * * * | 1 0  0  1 0 0
.. o.3o.3x.      4  0 |  0  6   0  0  0 |  0  0  4  0  0  0  0  0  0  0 | *  *  * 5  *  *  *  *  *  * * * | 1 0  0  0 1 0
xo3ox .. ..&#x   3  3 |  3  0   6  3  0 |  1  0  0  3  3  0  0  1  0  0 | *  *  * * 20  *  *  *  *  * * * | 0 1  1  0 0 0
xo .. ox ..&#x   2  2 |  1  0   4  0  1 |  0  0  0  2  0  2  0  0  0  0 | *  *  * *  * 30  *  *  *  * * * | 0 1  0  1 0 0
xo .. .. xo&#x   4  1 |  2  2   4  0  0 |  0  1  0  2  0  0  2  0  0  0 | *  *  * *  *  * 30  *  *  * * * | 0 0  1  1 0 0
.. ox3ox ..&#x   1  6 |  0  0   6  3  3 |  0  0  0  0  3  3  0  0  1  0 | *  *  * *  *  *  * 20  *  * * * | 0 1  0  0 1 0
.. ox .. xo&#x   2  2 |  0  1   4  1  0 |  0  0  0  0  2  0  2  0  0  0 | *  *  * *  *  *  *  * 30  * * * | 0 0  1  0 1 0
.. .. ox3xo&#x   3  3 |  0  3   6  0  3 |  0  0  1  0  0  3  3  0  0  1 | *  *  * *  *  *  *  *  * 20 * * | 0 0  0  1 1 0
.o3.x3.x ..      0 12 |  0  0   0 12  6 |  0  0  0  0  0  0  0  4  4  0 | *  *  * *  *  *  *  *  *  * 5 * | 0 1  0  0 0 1
.. .x3.x3.o      0 12 |  0  0   0  6 12 |  0  0  0  0  0  0  0  0  4  4 | *  *  * *  *  *  *  *  *  * * 5 | 0 0  0  0 1 1
---------------+-------+-----------------+-------------------------------+---------------------------------+--------------
x.3o.3o.3x.     20  0 | 30 30   0  0  0 | 20 30 20  0  0  0  0  0  0  0 | 5 10 10 5  0  0  0  0  0  0 0 0 | 1 *  *  * * *
xo3ox3ox ..&#x   4 12 |  6  0  24 12  6 |  4  0  0 12 12 12  0  4  4  0 | 1  0  0 0  4  6  0  4  0  0 1 0 | * 5  *  * * *
xo3ox .. xo&#x   6  3 |  6  3  12  3  0 |  2  3  0  6  6  0  6  1  0  0 | 0  1  0 0  2  0  3  0  3  0 0 0 | * * 10  * * *
xo .. ox3xo&#x   6  3 |  3  6  12  0  3 |  0  3  2  6  0  6  6  0  0  1 | 0  0  1 0  0  3  3  0  0  2 0 0 | * *  * 10 * *
.. ox3ox3xo&#x   4 12 |  0  6  24  6 12 |  0  0  4  0 12 12 12  0  4  4 | 0  0  0 1  0  0  0  4  6  4 0 1 | * *  *  * 5 *
.o3.x3.x3.o      0 30 |  0  0   0 30 30 |  0  0  0  0  0  0  0 10 20 10 | 0  0  0 0  0  0  0  0  0  0 5 5 | * *  *  * * 1
or
o.3o.3o.3o.      | 20  * |  6   6  0 |  6  6  12   6  0  0 |  2  6  6  6  6  1  0 | 1  2  6 0
.o3.o3.o3.o      |  * 30 |  0   4  4 |  0  0   4   8  2  4 |  0  0  4  4  1  4  4 | 0  4  2 1
-----------------+-------+-----------+---------------------+----------------------+----------
x. .. .. ..    & |  2  0 | 60   *  * |  2  2   2   0  0  0 |  1  3  2  1  2  0  0 | 1  1  3 0
oo3oo3oo3oo&#x   |  1  1 |  * 120  * |  0  0   2   2  0  0 |  0  0  2  2  1  1  0 | 0  2  2 0
.. .x .. ..    & |  0  2 |  *   * 60 |  0  0   0   2  1  2 |  0  0  2  1  0  2  3 | 0  3  1 1
-----------------+-------+-----------+---------------------+----------------------+----------
x.3o. .. ..    & |  3  0 |  3   0  0 | 40  *   *   *  *  * |  1  1  1  0  0  0  0 | 1  1  1 0
x. .. .. x.      |  4  0 |  4   0  0 |  * 30   *   *  *  * |  0  2  0  0  1  0  0 | 1  0  2 0
xo .. .. ..&#x & |  2  1 |  1   2  0 |  *  * 120   *  *  * |  0  0  1  1  1  0  0 | 0  1  2 0
.. ox .. ..&#x & |  1  2 |  0   2  1 |  *  *   * 120  *  * |  0  0  1  1  0  1  0 | 0  2  1 0
.o3.x .. ..    & |  0  3 |  0   0  3 |  *  *   *   * 20  * |  0  0  2  0  0  0  2 | 0  2  1 1
.. .x3.x ..      |  0  6 |  0   0  6 |  *  *   *   *  * 20 |  0  0  0  0  0  1  2 | 0  2  0 1
-----------------+-------+-----------+---------------------+----------------------+----------
x.3o.3o. ..    &   4  0 |  6   0  0 |  4  0   0   0  0  0 | 10  *  *  *  *  *  * | 1  1  0 0
x.3o. .. x.    &   6  0 |  9   0  0 |  2  3   0   0  0  0 |  * 20  *  *  *  *  * | 1  0  1 0
xo3ox .. ..&#x &   3  3 |  3   6  3 |  1  0   3   3  1  0 |  *  * 40  *  *  *  * | 0  1  1 0
xo .. ox ..&#x &   2  2 |  1   4  1 |  0  0   2   2  0  0 |  *  *  * 60  *  *  * | 0  1  1 0
xo .. .. xo&#x     4  1 |  4   4  0 |  0  1   4   0  0  0 |  *  *  *  * 30  *  * | 0  0  2 0
.. ox3ox ..&#x     1  6 |  0   6  6 |  0  0   0   6  0  1 |  *  *  *  *  * 20  * | 0  2  0 0
.o3.x3.x ..    &   0 12 |  0   0 18 |  0  0   0   0  4  4 |  *  *  *  *  *  * 10 | 0  1  0 1
-----------------+-------+-----------+---------------------+----------------------+----------
x.3o.3o.3x.       20  0 | 60   0  0 | 40 30   0   0  0  0 | 10 20  0  0  0  0  0 | 1  *  * *
xo3ox3ox ..&#x &   4 12 |  6  24 18 |  4  0  12  24  4  4 |  1  0  4  6  0  4  1 | * 10  * *
xo3ox .. xo&#x &   6  3 |  9  12  3 |  2  3  12   6  1  0 |  0  1  2  3  3  0  0 | *  * 20 *
.o3.x3.x3.o        0 30 |  0   0 60 |  0  0   0   0 20 20 |  0  0  0  0  0  0 10 | *  *  * 1

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