Acronym spidpy
Name (degenerate) spid pyramid
Circumradius ∞   i.e. flat in euclidean space
Confer
general polytopal classes:
decomposition   lace simplices  

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

ox3oo3oo3ox&#x   → height = 0
(pt || spid)

o.3o.3o.3o.    | 1  *  20  0  0 | 30 30  0  0  0 | 20 30 20 0  0  0 0 | 5 10 10 5 0
.o3.o3.o3.o    | * 20 |  1  3  3 |  3  3  3  6  3 |  3  6  3 1  3  3 1 | 1  3  3 1 1
---------------+------+----------+----------------+--------------------+------------
oo3oo3oo3oo&#x | 1  1 | 20  *  *   3  3  0  0  0 |  3  6  3 0  0  0 0 | 1  3  3 1 0
.x .. .. ..    | 0  2 |  * 30  * |  1  0  2  2  0 |  2  2  0 1  2  1 0 | 1  2  1 0 1
.. .. .. .x    | 0  2 |  *  * 30 |  0  1  0  2  2 |  0  2  2 0  1  2 1 | 0  1  2 1 1
---------------+------+----------+----------------+--------------------+------------
ox .. .. ..&#x | 1  2 |  2  1  0 | 30  *  *  *  * |  2  2  0 0  0  0 0 | 1  2  1 0 0
.. .. .. ox&#x | 1  2 |  2  0  1 |  * 30  *  *  * |  0  2  2 0  0  0 0 | 0  1  2 1 0
.x3.o .. ..    | 0  3 |  0  3  0 |  *  * 20  *  * |  1  0  0 1  1  0 0 | 1  1  0 0 1
.x .. .. .x    | 0  4 |  0  2  2 |  *  *  * 30  * |  0  1  0 0  1  1 0 | 0  1  1 0 1
.. .. .o3.x    | 0  3 |  0  0  3 |  *  *  *  * 20 |  0  0  1 0  0  1 1 | 0  0  1 1 1
---------------+------+----------+----------------+--------------------+------------
ox3oo .. ..&#x  1  3 |  3  3  0 |  3  0  1  0  0 | 20  *  * *  *  * * | 1  1  0 0 0
ox .. .. ox&#x  1  4 |  4  2  2 |  2  2  0  1  0 |  * 30  * *  *  * * | 0  1  1 0 0
.. .. oo3ox&#x  1  3 |  3  0  3 |  0  3  0  0  1 |  *  * 20 *  *  * * | 0  0  1 1 0
.x3.o3.o ..     0  4 |  0  6  0 |  0  0  4  0  0 |  *  *  * 5  *  * * | 1  0  0 0 1
.x3.o .. .x     0  6 |  0  6  3 |  0  0  2  3  0 |  *  *  * * 10  * * | 0  1  0 0 1
.x .. .o3.x     0  6 |  0  3  6 |  0  0  0  3  2 |  *  *  * *  * 10 * | 0  0  1 0 1
.. .o3.o3.x     0  4 |  0  0  6 |  0  0  0  0  4 |  *  *  * *  *  * 5 | 0  0  0 1 1
---------------+------+----------+----------------+--------------------+------------
ox3oo3oo ..&#x  1  4 |  4  6  0 |  6  0  4  0  0 |  4  0  0 1  0  0 0 | 5  *  * * *
ox3oo .. ox&#x  1  6 |  6  6  3 |  6  3  2  3  0 |  2  3  0 0  1  0 0 | * 10  * * *
ox .. oo3ox&#x  1  6 |  6  3  6 |  3  6  0  3  2 |  0  3  2 0  0  1 0 | *  * 10 * *
.. oo3oo3ox&#x  1  4 |  4  0  6 |  0  6  0  0  4 |  0  0  4 0  0  0 1 | *  *  * 5 *
.x3.o3.o3.x     0 20 |  0 30 30 |  0  0 20 30 20 |  0  0  0 5 10 10 5 | *  *  * * 1
or
o.3o.3o.3o.      | 1  *  20  0 | 60  0  0 | 40 30  0  0 | 10 20 0
.o3.o3.o3.o      | * 20 |  1  6 |  6  6  6 |  6  6  2  6 |  2  6 1
-----------------+------+-------+----------+-------------+--------
oo3oo3oo3oo&#x   | 1  1 | 20  *   6  0  0 |  6  6  0  0 |  2  6 0
.x .. .. ..    & | 0  2 |  * 60 |  1  2  2 |  2  2  1  3 |  1  3 1
-----------------+------+-------+----------+-------------+--------
ox .. .. ..&#x & | 1  2 |  2  1 | 60  *  * |  2  2  0  0 |  1  3 0
.x3.o .. ..    & | 0  3 |  0  3 |  * 40  * |  1  0  1  1 |  1  1 1
.x .. .. .x      | 0  4 |  0  4 |  *  * 30 |  0  1  0  2 |  0  2 1
-----------------+------+-------+----------+-------------+--------
ox3oo .. ..    &  1  3 |  3  3 |  3  1  0 | 40  *  *  * |  1  1 0
ox .. .. ox&#x    1  4 |  4  4 |  4  0  1 |  * 30  *  * |  0  2 0
.x3.o3.o ..    &  0  4 |  0  6 |  0  4  0 |  *  * 10  * |  1  0 1
.x3.o .. .x    &  0  6 |  0  9 |  0  2  3 |  *  *  * 20 |  0  1 1
-----------------+------+-------+----------+-------------+--------
ox3oo3oo ..&#x &  1  4 |  4  6 |  6  4  0 |  4  0  1  0 | 10  * *
ox3oo .. ox&#x &  1  6 |  6  9 |  9  2  3 |  2  3  0  1 |  * 20 *
.x3.o3.o3.x       0 20 |  0 60 |  0 40 30 |  0  0 10 20 |  *  * 1

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