Acronym ..., tes || sadi Name tes atop sadi Circumradius ∞   i.e. flat in euclidean space Coordinates (1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign (central tes) (τ2/2, τ/2, 1/2, 0)     & even permutations, all changes of sign (outer sadi) where τ = (1+sqrt(5))/2 Confer related segmentotera: os3os4oo3xo&#x   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

```os3os3os4xo&#x   → height = 0

o.3o.3o.4o.      | 16  * |  4  12  0  0  0   0 |  6 12  6  12  12 12  0  0   0  0  0 | 4  4  4 12  12 12 12 12  0  0 0  0 | 1  1  4  6 4 0 12
demi( .o3.o3.o4.o    ) |  * 96 |  0   2  2  1  2   4 |  0  1  2   4   4  2  1  2   6  3  3 | 0  2  2  1   6  2  3  3  2  1 1  4 | 0  2  1  1 1 1  4
-----------------------+-------+---------------------+-------------------------------------+------------------------------------+------------------
.. .. .. x.      |  2  0 | 32   *  *  *  *   * |  3  3  0   0   0  3  0  0   0  0  0 | 3  0  0  6   0  3  3  3  0  0 0  0 | 1  0  1  3 3 0  3
demi( oo3oo3oo4oo&#x ) |  1  1 |  * 192  *  *  *   * |  0  1  1   2   2  1  0  0   0  0  0 | 0  1  1  1   3  2  2  2  0  0 0  0 | 0  1  1  1 1 0  3
.s .2 .s ..      |  0  2 |  *   * 96  *  *   * |  0  0  1   0   0  0  0  0   2  2  0 | 0  0  0  0   2  0  2  0  1  1 0  2 | 0  1  0  1 0 1  2
.. .. .s4.o      |  0  2 |  *   *  * 48  *   * |  0  0  0   0   0  2  0  0   0  2  2 | 0  0  0  1   0  0  2  2  0  1 1  2 | 0  0  0  1 1 1  2
sefa( .s3.s .. ..    ) |  0  2 |  *   *  *  * 96   * |  0  0  0   2   0  0  1  0   2  0  0 | 0  2  0  0   2  1  0  0  2  0 0  1 | 0  2  1  0 0 1  1
sefa( .. .s3.s ..    ) |  0  2 |  *   *  *  *  * 192 |  0  0  0   0   1  0  0  1   1  0  1 | 0  0  1  0   1  0  0  1  1  0 1  1 | 0  1  0  0 1 1  1
-----------------------+-------+---------------------+-------------------------------------+------------------------------------+------------------
.. .. o.4x.      |  4  0 |  4   0  0  0  0   0 | 24  *  *   *   *  *  *  *   *  *  * | 2  0  0  2   0  0  0  0  0  0 0  0 | 1  0  0  1 2 0  0
demi( .. .. .. xo&#x ) |  2  1 |  1   2  0  0  0   0 |  * 96  *   *   *  *  *  *   *  *  * | 0  0  0  1   0  2  1  1  0  0 0  0 | 0  0  1  1 1 0  2
os .2 os ..&#x   |  1  2 |  0   2  1  0  0   0 |  *  * 96   *   *  *  *  *   *  *  * | 0  0  0  0   2  0  2  0  0  0 0  0 | 0  1  0  1 0 0  2
sefa( os3os .. ..&#x ) |  1  2 |  0   2  0  0  1   0 |  *  *  * 192   *  *  *  *   *  *  * | 0  1  0  0   1  1  0  0  0  0 0  0 | 0  1  1  0 0 0  1
sefa( .. os3os ..&#x ) |  1  2 |  0   2  0  0  0   1 |  *  *  *   * 192  *  *  *   *  *  * | 0  0  1  0   1  0  0  1  0  0 0  0 | 0  1  0  0 1 0  1
sefa( .. .. os4xo&#x ) |  2  2 |  1   2  0  1  0   0 |  *  *  *   *   * 96  *  *   *  *  * | 0  0  0  1   0  0  1  1  0  0 0  0 | 0  0  0  1 1 0  1
.s3.s .. ..      |  0  3 |  0   0  0  0  3   0 |  *  *  *   *   *  * 32  *   *  *  * | 0  2  0  0   0  0  0  0  2  0 0  0 | 0  2  1  0 0 1  0
.. .s3.s ..      |  0  3 |  0   0  0  0  0   3 |  *  *  *   *   *  *  * 64   *  *  * | 0  0  1  0   0  0  0  0  1  0 1  0 | 0  1  0  0 1 1  0
sefa( .s3.s3.s ..    ) |  0  3 |  0   0  1  0  1   1 |  *  *  *   *   *  *  *  * 192  *  * | 0  0  0  0   1  0  0  0  1  0 0  1 | 0  1  0  0 0 1  1
sefa( .s .2 .s4.o    ) |  0  3 |  0   0  2  1  0   0 |  *  *  *   *   *  *  *  *   * 96  * | 0  0  0  0   0  0  1  0  0  1 0  1 | 0  0  0  1 0 1  1
sefa( .. .s3.s4.o    ) |  0  3 |  0   0  0  1  0   2 |  *  *  *   *   *  *  *  *   *  * 96 | 0  0  0  0   0  0  0  1  0  0 1  1 | 0  0  0  0 1 1  1
-----------------------+-------+---------------------+-------------------------------------+------------------------------------+------------------
.. o.3o.4x.      ♦  8  0 | 12   0  0  0  0   0 |  6  0  0   0   0  0  0  0   0  0  0 | 8  *  *  *   *  *  *  *  *  * *  * | 1  0  0  0 1 0  0
os3os .. ..&#x   ♦  1  3 |  0   3  0  0  3   0 |  0  0  0   3   0  0  1  0   0  0  0 | * 64  *  *   *  *  *  *  *  * *  * | 0  1  1  0 0 0  0
.. os3os ..&#x   ♦  1  3 |  0   3  0  0  0   3 |  0  0  0   0   3  0  0  1   0  0  0 | *  * 64  *   *  *  *  *  *  * *  * | 0  1  0  0 1 0  0
.. .. os4xo&#x   ♦  4  2 |  4   4  0  1  0   0 |  1  2  0   0   0  2  0  0   0  0  0 | *  *  * 48   *  *  *  *  *  * *  * | 0  0  0  1 1 0  0
sefa( os3os3os ..&#x ) ♦  1  3 |  0   3  1  0  1   1 |  0  0  1   1   1  0  0  0   1  0  0 | *  *  *  * 192  *  *  *  *  * *  * | 0  1  0  0 0 0  1
sefa( os3os .2 xo&#x ) ♦  2  2 |  1   4  0  0  1   0 |  0  2  0   2   0  0  0  0   0  0  0 | *  *  *  *   * 96  *  *  *  * *  * | 0  0  1  0 0 0  1
sefa( os .2 os4xo&#x ) ♦  2  3 |  1   4  2  1  0   0 |  0  1  2   0   0  1  0  0   0  1  0 | *  *  *  *   *  * 96  *  *  * *  * | 0  0  0  1 0 0  1
sefa( .. os3os4xo&#x ) ♦  2  3 |  1   4  0  1  0   2 |  0  1  0   0   2  1  0  0   0  0  1 | *  *  *  *   *  *  * 96  *  * *  * | 0  0  0  0 1 0  1
.s3.s3.s ..      ♦  0 12 |  0   0  6  0 12  12 |  0  0  0   0   0  0  4  4  12  0  0 | *  *  *  *   *  *  *  * 16  * *  * | 0  1  0  0 0 1  0
.s .2 .s4.o      ♦  0  4 |  0   0  4  2  0   0 |  0  0  0   0   0  0  0  0   0  4  0 | *  *  *  *   *  *  *  *  * 24 *  * | 0  0  0  1 0 1  0
.. .s3.s4.o      ♦  0 12 |  0   0  0  6  0  24 |  0  0  0   0   0  0  0  8   0  0 12 | *  *  *  *   *  *  *  *  *  * 8  * | 0  0  0  0 1 1  0
sefa( .s3.s3.s4.o    ) ♦  0  4 |  0   0  2  1  1   2 |  0  0  0   0   0  0  0  0   2  1  1 | *  *  *  *   *  *  *  *  *  * * 96 | 0  0  0  0 0 1  1
-----------------------+-------+---------------------+-------------------------------------+------------------------------------+------------------
o.3o.3o.4x.      ♦ 16  0 | 32   0  0  0  0   0 | 24  0  0   0   0  0  0  0   0  0  0 | 8  0  0  0   0  0  0  0  0  0 0  0 | 1  *  *  * * *  *
os3os3os ..&#x   ♦  1 12 |  0  12  6  0 12  12 |  0  0  6  12  12  0  4  4  12  0  0 | 0  4  4  0  12  0  0  0  1  0 0  0 | * 16  *  * * *  *
os3os .2 xo&#x   ♦  2  3 |  1   6  0  0  3   0 |  0  3  0   6   0  0  1  0   0  0  0 | 0  2  0  0   0  3  0  0  0  0 0  0 | *  * 32  * * *  *
os .2 os4xo&#x   ♦  4  4 |  4   8  4  2  0   0 |  1  4  4   0   0  4  0  0   0  4  0 | 0  0  0  2   0  0  4  0  0  1 0  0 | *  *  * 24 * *  *
.. os3os4xo&#x   ♦  8 12 | 12  24  0  6  0  24 |  6 12  0   0  24 12  0  8   0  0 12 | 1  0  8  6   0  0  0 12  0  0 1  0 | *  *  *  * 8 *  *
.s3.s3.s4.o      ♦  0 96 |  0   0 96 48 96 192 |  0  0  0   0   0  0 32 64 192 96 96 | 0  0  0  0   0  0  0  0 16 24 8 96 | *  *  *  * * 1  *
sefa( os3os3os4xo&#x ) ♦  2  4 |  1   6  2  1  1   2 |  0  2  2   2   2  1  0  0   2  1  1 | 0  0  0  0   2  1  1  1  0  0 0  1 | *  *  *  * * * 96

starting figure: ox3ox3ox4xo&#x (which as a throughout unit-edged figure could be realized within hyperbolic space only)
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