Acronym ..., ico || sadi
Name ico atop sadi
Circumradius ∞   i.e. flat in euclidean space
Coordinates
  1. (1, 0, 0, 0)                & all permutations, all changes of sign
    (vertex inscribed 1/q-hex of central ico)
  2. (1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
    (vertex inscribed tes of central ico)
  3. 2/2, τ/2, 1/2, 0)     & even permutations, all changes of sign
    (outer sadi)
where τ = (1+sqrt(5))/2
Confer
related segmentotera:
os3os4xo3oo&#x   os3os3os4xo&#x  

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

os3os4oo3xo&#x   → height = 0
(ico || sadi)

      o.3o.4o.3o.      | 24  * |  8  12   0   0 | 12  24   6  24  0   0  0 |  6 12   8  12  24 12  0  0  0 | 1  1  8  6 0 12
demi( .o3.o4.o3.o    ) |  * 96 |  0   3   3   6 |  0   3   3  12  3   9  3 |  0  1   6   9   6  3  3  1  4 | 0  3  3  1 1  4
-----------------------+-------+----------------+--------------------------+-------------------------------+----------------
      .. .. .. x.      |  2  0 | 96   *   *   * |  3   3   0   0  0   0  0 |  3  3   0   0   3  3  0  0  0 | 1  0  1  3 0  3
demi( oo3oo4oo3oo&#x ) |  1  1 |  * 288   *   * |  0   2   1   4  0   0  0 |  0  1   2   3   4  2  0  0  0 | 0  1  2  1 0  3
      .. .s4.o ..      |  0  2 |  *   * 144   * |  0   0   1   0  0   2  2 |  0  0   0   2   0  2  1  1  2 | 0  1  0  1 1  2
sefa( .s3.s .. ..    ) |  0  2 |  *   *   * 288 |  0   0   0   2  1   2  0 |  0  0   2   2   1  0  2  0  1 | 0  2  1  0 1  1
-----------------------+-------+----------------+--------------------------+-------------------------------+----------------
      .. .. o.3x.      |  3  0 |  3   0   0   0 | 96   *   *   *  *   *  * |  2  1   0   0   0  1  0  0  0 | 1  0  0  2 0  1
demi( .. .. .. xo&#x ) |  2  1 |  1   2   0   0 |  * 288   *   *  *   *  * |  0  1   0   0   2  1  0  0  0 | 0  0  1  1 0  2
      .. os4oo ..&#x   |  1  2 |  0   2   1   0 |  *   * 144   *  *   *  * |  0  0   0   2   0  2  0  0  0 | 0  1  0  1 0  2
sefa( os3os .. ..&#x ) |  1  2 |  0   2   0   1 |  *   *   * 576  *   *  * |  0  0   1   1   1  0  0  0  0 | 0  1  1  0 0  1
      .s3.s .. ..      |  0  3 |  0   0   0   3 |  *   *   *   * 96   *  * |  0  0   2   0   0  0  2  0  0 | 0  2  1  0 1  0
sefa( .s3.s4.o ..    ) |  0  3 |  0   0   1   2 |  *   *   *   *  * 288  * |  0  0   0   1   0  0  1  0  1 | 0  1  0  0 1  1
sefa( .. .s4.o3.o    ) |  0  3 |  0   0   3   0 |  *   *   *   *  *   * 96 |  0  0   0   0   0  1  0  1  1 | 0  0  0  1 1  1
-----------------------+-------+----------------+--------------------------+-------------------------------+----------------
      .. o.4o.3x.        6  0 | 12   0   0   0 |  8   0   0   0  0   0  0 | 24  *   *   *   *  *  *  *  * | 1  0  0  1 0  0
demi( .. .. oo3xo&#x )   3  1 |  3   3   0   0 |  1   3   0   0  0   0  0 |  * 96   *   *   *  *  *  *  * | 0  0  0  1 0  1
      os3os .. ..&#x     1  3 |  0   3   0   3 |  0   0   0   3  1   0  0 |  *  * 192   *   *  *  *  *  * | 0  1  1  0 0  0
sefa( os3os4oo ..&#x )   1  3 |  0   3   1   2 |  0   0   1   2  0   1  0 |  *  *   * 288   *  *  *  *  * | 0  1  0  0 0  1
sefa( os3os .2 xo&#x )   2  2 |  1   4   0   1 |  0   2   0   2  0   0  0 |  *  *   *   * 288  *  *  *  * | 0  0  1  0 0  1
sefa( .. os4oo3xo&#x )   3  3 |  3   6   3   0 |  1   3   3   0  0   0  1 |  *  *   *   *   * 96  *  *  * | 0  0  0  1 0  1
      .s3.s4.o ..        0 12 |  0   0   6  24 |  0   0   0   0  8  12  0 |  *  *   *   *   *  * 24  *  * | 0  1  0  0 1  0
      .. .s4.o3.o        0  4 |  0   0   6   0 |  0   0   0   0  0   0  4 |  *  *   *   *   *  *  * 24  * | 0  0  0  1 1  0
sefa( .s3.s4.o3.o    )   0  4 |  0   0   3   3 |  0   0   0   0  0   3  1 |  *  *   *   *   *  *  *  * 96 | 0  0  0  0 1  1
-----------------------+-------+----------------+--------------------------+-------------------------------+----------------
      o.3o.4o.3x.       24  0 | 96   0   0   0 | 96   0   0   0  0   0  0 | 24  0   0   0   0  0  0  0  0 | 1  *  *  * *  *
      os3os4oo ..&#x     1 12 |  0  12   6  24 |  0   0   6  24  8  12  0 |  0  0   8  12   0  0  1  0  0 | * 24  *  * *  *
      os3os .2 xo&#x     2  3 |  1   6   0   3 |  0   3   0   6  1   0  0 |  0  0   2   0   3  0  0  0  0 | *  * 96  * *  *
      .. os4oo3xo&#x     6  4 | 12  12   6   0 |  8  12   6   0  0   0  4 |  1  4   0   0   0  4  0  1  0 | *  *  * 24 *  *
      .s3.s4.o3.o        0 96 |  0   0 144 288 |  0   0   0   0 96 288 96 |  0  0   0   0   0  0 24 24 96 | *  *  *  * 1  *
sefa( os3os4oo3xo&#x )   3  4 |  3   9   3   3 |  1   6   3   6  0   3  1 |  0  1   0   3   3  1  0  0  1 | *  *  *  * * 96

starting figure: ox3ox4oo3xo&#x (which as a throughout unit-edged figure could be realized within hyperbolic space only)

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