Acronym icaf (alt.: icalicope)
Name icositetrachoron antifastegium,
icositetrachoron atop inverted icositetrachoral-prism
Circumradius sqrt[(6+2 sqrt(2))/7] = 1.123033
Lace city
in approx. ASCII-art
i  
  I
i 

where:
i = x3o4o3o (ico)
I = o3o4o3x (dual ico)
o  c  Q  c  o		-- o x3o4o3o (ico)
             
  O   C   O  		-- x o3o4o3x (dual icope)

where:
o = o o3o4o (point)
c = o o3o4x (cube)
O = x x3o4o (ope)
Q = o q3o4o (q-oct)
C = x o3x4o (cope)
Confer
general polytopal classes:
antifastegia   segmentopeta  

Incidence matrix according to Dynkin symbol

ox xo3oo4oo3ox&#x   → height = sqrt[4 sqrt(2)-5] = 0.405233
(ico || dual icope)

o. o.3o.4o.3o.    | 24  *   8  12  0   0 | 12   6  48  24  0   0 |  6  24  12  48  48  16  0  0 | 1  24  24   8 12  24  16  2  0 0 |  6 12  8  1 2 0
.o .o3.o4.o3.o    |  * 48 |  0   6  1   8 |  0   6  12  24  8  12 |  0  12  24   8  24  24 12  6 | 0   8  24  24  1   8  12  6  6 1 |  1  8 12  6 1 1
------------------+-------+---------------+-----------------------+------------------------------+----------------------------------+----------------
.. x. .. .. ..    |  2  0 | 96   *  *   * |  3   0   6   0  0   0 |  3   3   0  12   6   0  0  0 | 1   6   3   0  6   6   2  0  0 0 |  3  3  1  0 2 0
oo oo3oo4oo3oo&#x |  1  1 |  * 288  *   * |  0   1   4   4  0   0 |  0   4   4   4   8   4  0  0 | 0   4   8   4  1   4   4  1  0 0 |  1  4  4  1 1 0
.x .. .. .. ..    |  0  2 |  *   * 24   * |  0   6   0   0  8   0 |  0  12  24   0   0   0 12  0 | 0   8  24  24  0   0   0  0  6 0 |  1  8 12  6 0 1
.. .. .. .. .x    |  0  2 |  *   *  * 192 |  0   0   0   3  1   3 |  0   0   3   0   3   6  3  3 | 0   0   3   6  0   1   3  3  3 1 |  0  1  3  3 1 1
------------------+-------+---------------+-----------------------+------------------------------+----------------------------------+----------------
.. x.3o. .. ..    |  3  0 |  3   0  0   0 | 96   *   *   *  *   * |  2   0   0   4   0   0  0  0 | 1   2   0   0  4   2   0  0  0 0 |  2  1  0  0 2 0
ox .. .. .. ..&#x |  1  2 |  0   2  1   0 |  * 144   *   *  *   * |  0   4   4   0   0   0  0  0 | 0   4   8   4  0   0   0  0  0 0 |  1  4  4  1 0 0
.. xo .. .. ..&#x |  2  1 |  1   2  0   0 |  *   * 576   *  *   * |  0   1   0   2   2   0  0  0 | 0   2   2   0  1   2   1  0  0 0 |  1  2  1  0 1 0
.. .. .. .. ox&#x |  1  2 |  0   2  0   1 |  *   *   * 576  *   * |  0   0   1   0   2   2  0  0 | 0   0   2   2  0   1   2  1  0 0 |  0  1  2  1 1 0
.x .. .. .. .x    |  0  4 |  0   0  2   2 |  *   *   *   * 96   * |  0   0   3   0   0   0  3  0 | 0   0   3   6  0   0   0  0  3 0 |  0  1  3  3 0 1
.. .. .. .o3.x    |  0  3 |  0   0  0   3 |  *   *   *   *  * 192 |  0   0   0   0   0   2  1  2 | 0   0   0   2  0   0   1  2  2 1 |  0  0  1  2 1 1
------------------+-------+---------------+-----------------------+------------------------------+----------------------------------+----------------
.. x.3o.4o. ..      6  0 | 12   0  0   0 |  8   0   0   0  0   0 | 24   *   *   *   *   *  *  * | 1   0   0   0  2   0   0  0  0 0 |  1  0  0  0 2 0
ox xo .. .. ..&#x   2  2 |  1   4  1   0 |  0   2   2   0  0   0 |  * 288   *   *   *   *  *  * | 0   2   2   0  0   0   0  0  0 0 |  1  2  1  0 0 0
ox .. .. .. ox&#x   1  4 |  0   4  2   2 |  0   2   0   2  1   0 |  *   * 288   *   *   *  *  * | 0   0   2   2  0   0   0  0  0 0 |  0  1  2  1 0 0
.. xo3oo .. ..&#x   3  1 |  3   3  0   0 |  1   0   3   0  0   0 |  *   *   * 384   *   *  *  * | 0   1   0   0  1   1   0  0  0 0 |  1  1  0  0 1 0
.. xo .. .. ox&#x   2  2 |  1   4  0   1 |  0   0   2   2  0   0 |  *   *   *   * 576   *  *  * | 0   0   1   0  0   1   1  0  0 0 |  0  1  1  0 1 0
.. .. .. oo3ox&#x   1  3 |  0   3  0   3 |  0   0   0   3  0   1 |  *   *   *   *   * 384  *  * | 0   0   0   1  0   0   1  1  0 0 |  0  0  1  1 1 0
.x .. .. .o3.x      0  6 |  0   0  3   6 |  0   0   0   0  3   2 |  *   *   *   *   *   * 96  * | 0   0   0   2  0   0   0  0  2 0 |  0  0  1  2 0 1
.. .. .o4.o3.x      0  6 |  0   0  0  12 |  0   0   0   0  0   8 |  *   *   *   *   *   *  * 48 | 0   0   0   0  0   0   0  1  1 1 |  0  0  0  1 1 1
------------------+-------+---------------+-----------------------+------------------------------+----------------------------------+----------------
.. x.3o.4o.3o.     24  0 | 96   0  0   0 | 96   0   0   0  0   0 | 24   0   0   0   0   0  0  0 | 1   *   *   *  *   *   *  *  * * |  0  0  0  0 2 0
ox xo3oo .. ..&#x   3  2 |  3   6  1   0 |  1   3   6   0  0   0 |  0   3   0   2   0   0  0  0 | * 192   *   *  *   *   *  *  * * |  1  1  0  0 0 0
ox xo .. .. ox&#x   2  4 |  1   8  2   2 |  0   4   4   4  1   0 |  0   2   2   0   2   0  0  0 | *   * 288   *  *   *   *  *  * * |  0  1  1  0 0 0
ox .. .. oo3ox&#x   1  6 |  0   6  3   6 |  0   3   0   6  3   2 |  0   0   3   0   0   2  1  0 | *   *   * 192  *   *   *  *  * * |  0  0  1  1 0 0
.. xo3oo4oo ..&#x   6  1 | 12   6  0   0 |  8   0  12   0  0   0 |  1   0   0   8   0   0  0  0 | *   *   *   * 48   *   *  *  * * |  1  0  0  0 1 0
.. xo3oo .. ox&#x   3  2 |  3   6  0   1 |  1   0   6   3  0   0 |  0   0   0   2   3   0  0  0 | *   *   *   *  * 192   *  *  * * |  0  1  0  0 1 0
.. xo .. oo3ox&#x   2  3 |  1   6  0   3 |  0   0   3   6  0   1 |  0   0   0   0   3   2  0  0 | *   *   *   *  *   * 192  *  * * |  0  0  1  0 1 0
.. .. oo4oo3ox&#x   1  6 |  0   6  0  12 |  0   0   0  12  0   8 |  0   0   0   0   0   8  0  1 | *   *   *   *  *   *   * 48  * * |  0  0  0  1 1 0
.x .. .o4.o3.x      0 12 |  0   0  6  24 |  0   0   0   0 12  16 |  0   0   0   0   0   0  8  2 | *   *   *   *  *   *   *  * 24 * |  0  0  0  1 0 1
.. .o3.o4.o3.x      0 24 |  0   0  0  96 |  0   0   0   0  0  96 |  0   0   0   0   0   0  0 24 | *   *   *   *  *   *   *  *  * 2 |  0  0  0  0 1 1
------------------+-------+---------------+-----------------------+------------------------------+----------------------------------+----------------
ox xo3oo4oo ..&#x   6  2 | 12  12  1   0 |  8   6  24   0  0   0 |  1  12   0  16   0   0  0  0 | 0   8   0   0  2   0   0  0  0 0 | 24  *  *  * * *
ox xo3oo .. ox&#x   3  4 |  3  12  2   2 |  1   6  12   6  1   0 |  0   6   3   4   6   0  0  0 | 0   2   3   0  0   2   0  0  0 0 |  * 96  *  * * *
ox xo .. oo3ox&#x   2  6 |  1  12  3   6 |  0   6   6  12  3   2 |  0   3   6   0   6   4  1  0 | 0   0   3   2  0   0   2  0  0 0 |  *  * 96  * * *
ox .. oo4oo3ox&#x   1 12 |  0  12  6  24 |  0   6   0  24 12  16 |  0   0  12   0   0  16  8  2 | 0   0   0   8  0   0   0  2  1 0 |  *  *  * 24 * *
.. xo3oo4oo3ox&#x  24 24 | 96 144  0  96 | 96   0 288 288  0  96 | 24   0   0 192 288 192  0 24 | 1   0   0   0 24  96  96 24  0 1 |  *  *  *  * 2 *
.x .o3.o4.o3.x      0 48 |  0   0 24 192 |  0   0   0   0 96 192 |  0   0   0   0   0   0 96 48 | 0   0   0   0  0   0   0  0 24 2 |  *  *  *  * * 1

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