Acronym	tespy
Name	(degenerate) tes pyramid
Circumradius	∞   i.e. flat in euclidean space
Coordinates	(1/2, 1/2, 1/2, 1/2)   & all changes of sign (0, 0, 0, 0)
Face vector	17, 48, 56, 32, 9
Confer	general polytopal classes: fundamental lace prisms   lace simplices   decomposition
External links

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

oo3oo3oo4ox&#x   → height = 0
(pt || tes)

o.3o.3o.4o.    | 1  * ♦ 16  0 | 32  0 | 24 0 | 8 0
.o3.o3.o4.o    | * 16 |  1  4 |  4  6 |  6 4 | 4 1
---------------+------+-------+-------+------+----
oo3oo3oo4oo&#x | 1  1 | 16  * ♦  4  0 |  6 0 | 4 0
.. .. .. .x    | 0  2 |  * 32 |  1  3 |  3 3 | 3 1
---------------+------+-------+-------+------+----
.. .. .. ox&#x | 1  2 |  2  1 | 32  * |  3 0 | 3 0
.. .. .o4.x    | 0  4 |  0  4 |  * 24 |  1 2 | 2 1
---------------+------+-------+-------+------+----
.. .. oo4ox&#x ♦ 1  4 |  4  4 |  4  1 | 24 * | 2 0
.. .o3.o4.x    ♦ 0  8 |  0 12 |  0  6 |  * 8 | 1 1
---------------+------+-------+-------+------+----
.. oo3oo4ox&#x ♦ 1  8 |  8 12 | 12  6 |  6 1 | 8 *
.o3.o3.o4.x    ♦ 0 16 |  0 32 |  0 24 |  0 8 | * 1

ox oo3oo4ox&#x   → height = 0
(pt || tes)

o. o.3o.4o.    | 1  * ♦ 16 0  0 | 8 24  0  0 | 12 12 0 0 | 6 2 0
.o .o3.o4.o    | * 16 |  1 1  3 | 1  3  3  3 |  3  3 3 1 | 3 1 1
---------------+------+---------+------------+-----------+------
oo oo3oo4oo&#x | 1  1 | 16 *  * ♦ 1  3  0  0 |  3  3 0 0 | 3 1 0
.x .. .. ..    | 0  2 |  * 8  * | 1  0  3  0 |  3  0 3 0 | 3 0 1
.. .. .. .x    | 0  2 |  * * 24 | 0  1  1  2 |  1  2 2 1 | 2 1 1
---------------+------+---------+------------+-----------+------
ox .. .. ..&#x | 1  2 |  2 1  0 | 8  *  *  * |  3  0 0 0 | 3 0 0
.. .. .. ox&#x | 1  2 |  2 0  1 | * 24  *  * |  1  2 0 0 | 2 1 0
.x .. .. .x    | 0  4 |  0 2  2 | *  * 12  * |  1  0 2 0 | 2 0 1
.. .. .o4.x    | 0  4 |  0 0  4 | *  *  * 12 |  0  1 1 1 | 1 1 1
---------------+------+---------+------------+-----------+------
ox .. .. ox&#x ♦ 1  4 |  4 2  2 | 2  2  1  0 | 12  * * * | 2 0 0
.. .. oo4ox&#x ♦ 1  4 |  4 0  4 | 0  4  0  1 |  * 12 * * | 1 1 0
.x .. .o4.x    ♦ 0  8 |  0 4  8 | 0  0  4  2 |  *  * 6 * | 1 0 1
.. .o3.o4.x    ♦ 0  8 |  0 0 12 | 0  0  0  6 |  *  * * 2 | 0 1 1
---------------+------+---------+------------+-----------+------
ox .. oo4ox&#x ♦ 1  8 |  8 4  8 | 4  8  4  2 |  4  2 1 0 | 6 * *
.. oo3oo4ox&#x ♦ 1  8 |  8 0 12 | 0 12  0  6 |  0  6 0 1 | * 2 *
.x .o3.o4.x    ♦ 0 16 |  0 8 24 | 0  0 12 12 |  0  0 6 2 | * * 1

ox4oo ox4oo&#x   → height = 0
(pt || tes)

o.4o. o.4o.    | 1  * ♦ 16  0  0 | 16 16 0  0 0 | 4 16 4 0 0 | 4 4 0
.o4.o .o4.o    | * 16 |  1  2  2 |  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
---------------+------+----------+--------------+------------+------
oo4oo oo4oo&#x | 1  1 | 16  *  * ♦  2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
.x .. .. ..    | 0  2 |  * 16  * |  1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
.. .. .x ..    | 0  2 |  *  * 16 |  0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
---------------+------+----------+--------------+------------+------
ox .. .. ..&#x | 1  2 |  2  1  0 | 16  * *  * * | 1  2 0 0 0 | 2 1 0
.. .. ox ..&#x | 1  2 |  2  0  1 |  * 16 *  * * | 0  2 1 0 0 | 1 2 0
.x4.o .. ..    | 0  4 |  0  4  0 |  *  * 4  * * | 1  0 0 2 0 | 2 0 1
.x .. .x ..    | 0  4 |  0  2  2 |  *  * * 16 * | 0  1 0 1 1 | 1 1 1
.. .. .x4.o    | 0  4 |  0  0  4 |  *  * *  * 4 | 0  0 1 0 2 | 0 2 1
---------------+------+----------+--------------+------------+------
ox4oo .. ..&#x ♦ 1  4 |  4  4  0 |  4  0 1  0 0 | 4  * * * * | 2 0 0
ox .. ox ..&#x ♦ 1  4 |  4  2  2 |  2  2 0  1 0 | * 16 * * * | 1 1 0
.. .. ox4oo&#x ♦ 1  4 |  4  0  4 |  0  4 0  0 1 | *  * 4 * * | 0 2 0
.x4.o .x ..    ♦ 0  8 |  0  8  4 |  0  0 2  4 0 | *  * * 4 * | 1 0 1
.x .. .x4.o    ♦ 0  8 |  0  4  8 |  0  0 0  4 2 | *  * * * 4 | 0 1 1
---------------+------+----------+--------------+------------+------
ox4oo ox ..&#x ♦ 1  8 |  8  8  4 |  8  4 2  4 0 | 2  4 0 1 0 | 4 * *
ox .. ox4oo&#x ♦ 1  8 |  8  4  8 |  4  8 0  4 2 | 0  4 2 0 1 | * 4 *
.x4.o .x4.o    ♦ 0 16 |  0 16 16 |  0  0 4 16 4 | 0  0 0 4 4 | * * 1

ox ox ox4oo&#x   → height = 0
(pt || tes)

... 

ox ox ox ox&#x   → height = 0
(pt || tes)

o. o. o. o.    | 1  * ♦ 16 0 0 0 0 | 8 8 8 8 0 0 0 0 0 0 | 4 4 4 4 4 4 0 0 0 0 | 2 2 2 2 0
.o .o .o .o    | * 16 |  1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
---------------+------+------------+---------------------+---------------------+----------
oo oo oo oo&#x | 1  1 | 16 * * * * ♦ 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
.x .. .. ..    | 0  2 |  * 8 * * * | 1 1 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1
.. .x .. ..    | 0  2 |  * * 8 * * | 0 1 0 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1
.. .. .x ..    | 0  2 |  * * * 8 * | 0 0 1 0 0 1 0 1 0 1 | 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1
.. .. .. .x    | 0  2 |  * * * * 8 | 0 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
---------------+------+------------+---------------------+---------------------+----------
ox .. .. ..&#x | 1  2 |  2 1 0 0 0 | 8 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
.. ox .. ..&#x | 1  2 |  2 0 1 0 0 | * 8 * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0
.. .. ox ..&#x | 1  2 |  2 0 0 1 0 | * * 8 * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0
.. .. .. ox&#x | 1  2 |  2 0 0 0 1 | * * * 8 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
.x .x .. ..    | 0  4 |  0 2 2 0 0 | * * * * 4 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
.x .. .x ..    | 0  4 |  0 2 0 2 0 | * * * * * 4 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1
.x .. .. .x    | 0  4 |  0 2 0 0 2 | * * * * * * 4 * * * | 0 0 1 0 0 0 0 1 0 1 | 0 1 0 1 1
.. .x .x ..    | 0  4 |  0 0 2 2 0 | * * * * * * * 4 * * | 0 0 0 1 0 0 1 0 1 0 | 1 0 1 0 1
.. .x .. .x    | 0  4 |  0 0 2 0 2 | * * * * * * * * 4 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
.. .. .x .x    | 0  4 |  0 0 0 2 2 | * * * * * * * * * 4 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+------+------------+---------------------+---------------------+----------
ox ox .. ..&#x ♦ 1  4 |  4 2 2 0 0 | 2 2 0 0 1 0 0 0 0 0 | 4 * * * * * * * * * | 1 1 0 0 0
ox .. ox ..&#x ♦ 1  4 |  4 2 0 2 0 | 2 0 2 0 0 1 0 0 0 0 | * 4 * * * * * * * * | 1 0 1 0 0
ox .. .. ox&#x ♦ 1  4 |  4 2 0 0 2 | 2 0 0 2 0 0 1 0 0 0 | * * 4 * * * * * * * | 0 1 0 1 0
.. ox ox ..&#x ♦ 1  4 |  4 0 2 2 0 | 0 2 2 0 0 0 0 1 0 0 | * * * 4 * * * * * * | 1 0 1 0 0
.. ox .. ox&#x ♦ 1  4 |  4 0 2 0 2 | 0 2 0 2 0 0 0 0 1 0 | * * * * 4 * * * * * | 0 1 0 1 0
.. .. ox ox&#x ♦ 1  4 |  4 0 0 2 2 | 0 0 2 2 0 0 0 0 0 1 | * * * * * 4 * * * * | 0 0 1 1 0
.x .x .x ..    ♦ 0  8 |  0 4 4 4 0 | 0 0 0 0 2 2 0 2 0 0 | * * * * * * 2 * * * | 1 0 0 0 1
.x .x .. .x    ♦ 0  8 |  0 4 4 0 4 | 0 0 0 0 2 0 2 0 2 0 | * * * * * * * 2 * * | 0 1 0 0 1
.x .. .x .x    ♦ 0  8 |  0 4 0 4 4 | 0 0 0 0 0 2 2 0 0 2 | * * * * * * * * 2 * | 0 0 1 0 1
.. .x .x .x    ♦ 0  8 |  0 0 4 4 4 | 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * 2 | 0 0 0 1 1
---------------+------+------------+---------------------+---------------------+----------
ox ox ox ..&#x ♦ 1  8 |  8 4 4 4 0 | 4 4 4 0 2 2 0 2 0 0 | 2 2 0 2 0 0 1 0 0 0 | 2 * * * *
ox ox .. ox&#x ♦ 1  8 |  8 4 4 0 4 | 4 4 0 4 2 0 2 0 2 0 | 2 0 2 0 2 0 0 1 0 0 | * 2 * * *
ox .. ox ox&#x ♦ 1  8 |  8 4 0 4 4 | 4 0 4 4 0 2 2 0 0 2 | 0 2 2 0 0 2 0 0 1 0 | * * 2 * *
.. ox ox ox&#x ♦ 1  8 |  8 0 4 4 4 | 0 4 4 4 0 0 0 2 2 2 | 0 0 0 2 2 2 0 0 0 1 | * * * 2 *
.x .x .x .x    ♦ 0 16 |  0 8 8 8 8 | 0 0 0 0 4 4 4 4 4 4 | 0 0 0 0 0 0 2 2 2 2 | * * * * 1