Acronym ricasrit, rico || srit
Name rectified-icositetrachoron atop small-rhombated-tesseract
Circumradius sqrt[2+sqrt(2)] = 1.847759
Lace city
in approx. ASCII-art
c   t   q   t   c		-- x3o3x4o (rico)
  s   T   T   s  		-- o3x3o4x (srit)

where:
c = o3x4o (co)
t = x3x4o (toe)
q = x3o4q ((x,q)-sirco)
s = x3o4x (sirco)
T = o3x4x (tic)
   c   t (u+U) t   c   		-- x3o3x4o (rico)
O  a  W b  D  B W  A  O		-- o3x3o4x (srit)

where:
c = x3o3x (co)
t = x3x3x (toe)
u = u3x3o ((u,x)-tut)
U = o3x3u (inv. (u,x)-tut)
O = o3x3o (oct)
a = o3x3q (inv. (q,x)-tut)
A = q3x3o ((q,x)-tut)
W = o3w3o (w-oct)
b = x3o3w ((x,w)-sirco)
B = w3o3x ((w,x)-sirco)
D = x3q3x ((q,x)-toe)
Confer
general polytopal classes:
segmentotera   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

xo3ox3xo4ox&#x   → height = sqrt[sqrt(2)-1] = 0.643594
(rico || srit)

o.3o.3o.4o.    | 96  * |  2   4   4   0  0 |  1  4  2  2   4   2   4   2  0  0  0  0 |  2  2 1  2  4  2  2  1  2  0  0 0 | 1  2  1  2 1 0
.o3.o3.o4.o    |  * 96 |  0   0   4   4  2 |  0  0  0  0   2   4   2   4  2  2  4  1 |  0  0 0  2  1  2  2  4  2  1  2 2 | 0  1  2  1 2 1
---------------+-------+-------------------+-----------------------------------------+-----------------------------------+---------------
x. .. .. ..    |  2  0 | 96   *   *   *  * |  1  2  0  0   2   0   0   0  0  0  0  0 |  2  1 0  2  2  1  0  0  0  0  0 0 | 1  2  1  1 0 0
.. .. x. ..    |  2  0 |  * 192   *   *  * |  0  1  1  1   0   0   1   0  0  0  0  0 |  1  1 1  0  1  0  1  0  1  0  0 0 | 1  1  0  1 1 0
oo3oo3oo4oo&#x |  1  1 |  *   * 384   *  * |  0  0  0  0   1   1   1   1  0  0  0  0 |  0  0 0  1  1  1  1  1  1  0  0 0 | 0  1  1  1 1 0
.. .x .. ..    |  0  2 |  *   *   * 192  * |  0  0  0  0   0   1   0   0  1  1  1  0 |  0  0 0  1  0  0  1  1  0  1  1 1 | 0  1  1  0 1 1
.. .. .. .x    |  0  2 |  *   *   *   * 96 |  0  0  0  0   0   0   0   2  0  0  2  1 |  0  0 0  0  0  1  0  2  2  0  1 2 | 0  0  1  1 2 1
---------------+-------+-------------------+-----------------------------------------+-----------------------------------+---------------
x.3o. .. ..    |  3  0 |  3   0   0   0  0 | 32  *  *  *   *   *   *   *  *  *  *  * |  2  0 0  2  0  0  0  0  0  0  0 0 | 1  2  1  0 0 0
x. .. x. ..    |  4  0 |  2   2   0   0  0 |  * 96  *  *   *   *   *   *  *  *  *  * |  1  1 0  0  1  0  0  0  0  0  0 0 | 1  1  0  1 0 0
.. o.3x. ..    |  3  0 |  0   3   0   0  0 |  *  * 64  *   *   *   *   *  *  *  *  * |  1  0 1  0  0  0  1  0  0  0  0 0 | 1  1  0  0 1 0
.. .. x.4o.    |  4  0 |  0   4   0   0  0 |  *  *  * 48   *   *   *   *  *  *  *  * |  0  1 1  0  0  0  0  0  1  0  0 0 | 1  0  0  1 1 0
xo .. .. ..&#x |  2  1 |  1   0   2   0  0 |  *  *  *  * 192   *   *   *  *  *  *  * |  0  0 0  1  1  1  0  0  0  0  0 0 | 0  1  1  1 0 0
.. ox .. ..&#x |  1  2 |  0   0   2   1  0 |  *  *  *  *   * 192   *   *  *  *  *  * |  0  0 0  1  0  0  1  1  0  0  0 0 | 0  1  1  0 1 0
.. .. xo ..&#x |  2  1 |  0   1   2   0  0 |  *  *  *  *   *   * 192   *  *  *  *  * |  0  0 0  0  1  0  1  0  1  0  0 0 | 0  1  0  1 1 0
.. .. .. ox&#x |  1  2 |  0   0   2   0  1 |  *  *  *  *   *   *   * 192  *  *  *  * |  0  0 0  0  0  1  0  1  1  0  0 0 | 0  0  1  1 1 0
.o3.x .. ..    |  0  3 |  0   0   0   3  0 |  *  *  *  *   *   *   *   * 64  *  *  * |  0  0 0  1  0  0  0  0  0  1  1 0 | 0  1  1  0 0 1
.. .x3.o ..    |  0  3 |  0   0   0   3  0 |  *  *  *  *   *   *   *   *  * 64  *  * |  0  0 0  0  0  0  1  0  0  1  0 1 | 0  1  0  0 1 1
.. .x .. .x    |  0  4 |  0   0   0   2  2 |  *  *  *  *   *   *   *   *  *  * 96  * |  0  0 0  0  0  0  0  1  0  0  1 1 | 0  0  1  0 1 1
.. .. .o4.x    |  0  4 |  0   0   0   0  4 |  *  *  *  *   *   *   *   *  *  *  * 24 |  0  0 0  0  0  0  0  0  2  0  0 2 | 0  0  0  1 2 1
---------------+-------+-------------------+-----------------------------------------+-----------------------------------+---------------
x.3o.3x. ..     12  0 | 12  12   0   0  0 |  4  6  4  0   0   0   0   0  0  0  0  0 | 16  * *  *  *  *  *  *  *  *  * * | 1  1  0  0 0 0
x. .. x.4o.      8  0 |  4   8   0   0  0 |  0  4  0  2   0   0   0   0  0  0  0  0 |  * 24 *  *  *  *  *  *  *  *  * * | 1  0  0  1 0 0
.. o.3x.4o.     12  0 |  0  24   0   0  0 |  0  0  8  6   0   0   0   0  0  0  0  0 |  *  * 8  *  *  *  *  *  *  *  * * | 1  0  0  0 1 0
xo3ox .. ..&#x   3  3 |  3   0   6   3  0 |  1  0  0  0   3   3   0   0  1  0  0  0 |  *  * * 64  *  *  *  *  *  *  * * | 0  1  1  0 0 0
xo .. xo ..&#x   4  1 |  2   2   4   0  0 |  0  1  0  0   2   0   2   0  0  0  0  0 |  *  * *  * 96  *  *  *  *  *  * * | 0  1  0  1 0 0
xo .. .. ox&#x   2  2 |  1   0   4   0  1 |  0  0  0  0   2   0   0   2  0  0  0  0 |  *  * *  *  * 96  *  *  *  *  * * | 0  0  1  1 0 0
.. ox3xo ..&#x   3  3 |  0   3   6   3  0 |  0  0  1  0   0   3   3   0  0  1  0  0 |  *  * *  *  *  * 64  *  *  *  * * | 0  1  0  0 1 0
.. ox .. ox&#x   1  4 |  0   0   4   2  2 |  0  0  0  0   0   2   0   2  0  0  1  0 |  *  * *  *  *  *  * 96  *  *  * * | 0  0  1  0 1 0
.. .. xo4ox&#x   4  4 |  0   4   8   0  4 |  0  0  0  1   0   0   4   4  0  0  0  1 |  *  * *  *  *  *  *  * 48  *  * * | 0  0  0  1 1 0
.o3.x3.o ..      0  6 |  0   0   0  12  0 |  0  0  0  0   0   0   0   0  4  4  0  0 |  *  * *  *  *  *  *  *  * 16  * * | 0  1  0  0 0 1
.o3.x .. .x      0  6 |  0   0   0   6  3 |  0  0  0  0   0   0   0   0  2  0  3  0 |  *  * *  *  *  *  *  *  *  * 32 * | 0  0  1  0 0 1
.. .x3.o4.x      0 24 |  0   0   0  24 24 |  0  0  0  0   0   0   0   0  0  8 12  6 |  *  * *  *  *  *  *  *  *  *  * 8 | 0  0  0  0 1 1
---------------+-------+-------------------+-----------------------------------------+-----------------------------------+---------------
x.3o.3x.4o.     96  0 | 96 192   0   0  0 | 32 96 64 48   0   0   0   0  0  0  0  0 | 16 24 8  0  0  0  0  0  0  0  0 0 | 1  *  *  * * *
xo3ox3xo ..&#x  12  6 | 12  12  24  12  0 |  4  6  4  0  12  12  12   0  4  4  0  0 |  1  0 0  4  6  0  4  0  0  1  0 0 | * 16  *  * * *
xo3ox .. ox&#x   3  6 |  3   0  12   6  3 |  1  0  0  0   6   6   0   6  2  0  3  0 |  0  0 0  2  0  3  0  3  0  0  1 0 | *  * 32  * * *
xo .. xo4ox&#x   8  4 |  4   8  16   0  4 |  0  4  0  2   8   0   8   8  0  0  0  1 |  0  1 0  0  4  4  0  0  2  0  0 0 | *  *  * 24 * *
.. ox3xo4ox&#x  12 24 |  0  24  48  24 24 |  0  0  8  6   0  24  24  24  0  8 12  6 |  0  0 1  0  0  0  8 12  6  0  0 1 | *  *  *  * 8 *
.o3.x3.o4.x      0 96 |  0   0   0 192 96 |  0  0  0  0   0   0   0   0 64 64 96 24 |  0  0 0  0  0  0  0  0  0 16 32 8 | *  *  *  * * 1

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