Acronym icopy
Name (degenerate) ico pyramid
Circumradius ∞   i.e. flat in euclidean space
Confer
general polytopal classes:
fundamental lace prisms   lace simplices   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

ox3oo4oo3oo&#x   → height = 0
(pt || ico)

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

oo3ox3oo4oo&#x   → height = 0
(pt || ico)

o.3o.3o.4o.    | 1  *  24  0 | 96  0  0 | 32 64  0 0 | 16 8 0
.o3.o3.o4.o    | * 24   1  8 |  8  4  8 |  4  8  4 2 |  4 2 1
---------------+------+-------+----------+------------+-------
oo3oo3oo4oo&#x | 1  1 | 24  *   8  0  0 |  4  8  0 0 |  4 2 0
.. .x .. ..    | 0  2 |  * 96 |  1  1  2 |  1  2  2 1 |  2 1 1
---------------+------+-------+----------+------------+-------
.. ox .. ..&#x | 1  2 |  2  1 | 96  *  * |  1  2  0 0 |  2 1 0
.o3.x .. ..    | 0  3 |  0  3 |  * 32  * |  1  0  2 0 |  2 0 1
.. .x3.o ..    | 0  3 |  0  3 |  *  * 64 |  0  1  1 1 |  1 1 1
---------------+------+-------+----------+------------+-------
oo3ox .. ..&#x  1  3 |  3  3 |  3  1  0 | 32  *  * * |  2 0 0
.. ox3oo ..&#x  1  3 |  3  3 |  3  0  1 |  * 64  * * |  1 1 0
.o3.x3.o ..     0  6 |  0 12 |  0  4  4 |  *  * 16 * |  1 0 1
.. .x3.o4.o     0  6 |  0 12 |  0  0  8 |  *  *  * 8 |  0 1 1
---------------+------+-------+----------+------------+-------
oo3ox3oo ..&#x  1  6 |  6 12 | 12  4  4 |  4  4  1 0 | 16 * *
.. ox3oo4oo&#x  1  6 |  6 12 | 12  0  8 |  0  8  0 1 |  * 8 *
.o3.x3.o4.o     0 24 |  0 96 |  0 32 64 |  0  0 16 8 |  * * 1

oo3ox3oo *b3oo&#x   → height = 0
(pt || ico)

o.3o.3o. *b3o.    | 1  *  24  0 | 96  0  0  0 | 32 32 32 0 0 0 | 8 8 8 0
.o3.o3.o *b3.o    | * 24   1  8 |  8  4  4  4 |  4  4  4 2 2 2 | 2 2 2 1
------------------+------+-------+-------------+----------------+--------
oo3oo3oo *b3oo&#x | 1  1 | 24  *   8  0  0  0 |  4  4  4 0 0 0 | 2 2 2 0
.. .x ..    ..    | 0  2 |  * 96 |  1  1  1  1 |  1  1  1 1 1 1 | 1 1 1 1
------------------+------+-------+-------------+----------------+--------
.. ox ..    ..&#x | 1  2 |  2  1 | 96  *  *  * |  1  1  1 0 0 0 | 1 1 1 0
.o3.x ..    ..    | 0  3 |  0  3 |  * 32  *  * |  1  0  0 1 1 0 | 1 1 0 1
.. .x3.o    ..    | 0  3 |  0  3 |  *  * 32  * |  0  1  0 1 0 1 | 1 0 1 1
.. .x .. *b3.o    | 0  3 |  0  3 |  *  *  * 32 |  0  0  1 0 1 1 | 0 1 1 1
------------------+------+-------+-------------+----------------+--------
oo3ox ..    ..&#x  1  3 |  3  3 |  3  1  0  0 | 32  *  * * * * | 1 1 0 0
.. ox3oo    ..&#x  1  3 |  3  3 |  3  0  1  0 |  * 32  * * * * | 1 0 1 0
.. ox .. *b3oo&#x  1  3 |  3  3 |  3  0  0  1 |  *  * 32 * * * | 0 1 1 0
.o3.x3.o    ..     0  6 |  0 12 |  0  4  4  0 |  *  *  * 8 * * | 1 0 0 1
.o3.x .. *b3.o     0  6 |  0 12 |  0  4  0  4 |  *  *  * * 8 * | 0 1 0 1
.. .x3.o *b3.o     0  6 |  0 12 |  0  0  4  4 |  *  *  * * * 8 | 0 0 1 1
------------------+------+-------+-------------+----------------+--------
oo3ox3oo    ..&#x  1  6 |  6 12 | 12  4  4  0 |  4  4  0 1 0 0 | 8 * * *
oo3ox .. *b3oo&#x  1  6 |  6 12 | 12  4  0  4 |  4  0  4 0 1 0 | * 8 * *
.. ox3oo *b3oo&#x  1  6 |  6 12 | 12  0  4  4 |  0  4  4 0 0 1 | * * 8 *
.o3.x3.o *b3.o     0 24 |  0 96 |  0 32 32 32 |  0  0  0 8 8 8 | * * * 1

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