Acronym icoap (alt.: icoalico)
Name icositetrachoral antiprism,
icositetrachoron atop dual icositetrachoron
Circumradius sqrt[3+sqrt(2)]/2 = 1.050501
Lace city
in approx. ASCII-art
o  c  Q  c  o		-- x3o4o3o (ico)
             
  O   C   O  		-- o3o4o3x (dual ico)

where:
o = o3o4o (point)
c = o3o4x (cube)
O = x3o4o (oct)
Q = q3o4o (q-oct)
Dihedral angles
(at margins)
  • at oct between ico and octpy:   arccos[-(sqrt(2)-1)] = 114.469801°
  • ...
Confer
related segmentotera:
tes || ico  
general polytopal classes:
segmentotera   fundamental lace prisms   scaliform  

Incidence matrix according to Dynkin symbol

xo3oo4oo3ox&#x   → height = sqrt[sqrt(2)-1] = 0.643594
(ico || dual ico)

o.3o.4o.3o.    | 24  *   8   6  0 | 12  24  12  0 |  6  24  24   8  0 | 1  6 12  8  1 0
.o3.o4.o3.o    |  * 24   0   6  8 |  0  12  24 12 |  0   8  24  24  6 | 0  1  8 12  6 1
---------------+-------+-----------+---------------+-------------------+----------------
x. .. .. ..    |  2  0 | 96   *  * |  3   3   0  0 |  3   6   3   0  0 | 1  3  3  1  0 0
oo3oo4oo3oo&#x |  1  1 |  * 144  *   0   4   4  0 |  0   4   8   4  0 | 0  1  4  4  1 0
.. .. .. .x    |  0  2 |  *   * 96 |  0   0   3  3 |  0   0   3   6  3 | 0  0  1  3  3 1
---------------+-------+-----------+---------------+-------------------+----------------
x.3o. .. ..    |  3  0 |  3   0  0 | 96   *   *  * |  2   2   0   0  0 | 1  2  1  0  0 0
xo .. .. ..&#x |  2  1 |  1   2  0 |  * 288   *  * |  0   2   2   0  0 | 0  1  2  1  0 0
.. .. .. ox&#x |  1  2 |  0   2  1 |  *   * 288  * |  0   0   2   2  0 | 0  0  1  2  1 0
.. .. .o3.x    |  0  3 |  0   0  3 |  *   *   * 96 |  0   0   0   2  2 | 0  0  0  1  2 1
---------------+-------+-----------+---------------+-------------------+----------------
x.3o.4o. ..      6  0 | 12   0  0 |  8   0   0  0 | 24   *   *   *  * | 1  1  0  0  0 0
xo3oo .. ..&#x   3  1 |  3   3  0 |  1   3   0  0 |  * 192   *   *  * | 0  1  1  0  0 0
xo .. .. ox&#x   2  2 |  1   4  1 |  0   2   2  0 |  *   * 288   *  * | 0  0  1  1  0 0
.. .. oo3ox&#x   1  3 |  0   3  3 |  0   0   3  1 |  *   *   * 192  0 | 0  0  0  1  1 0
.. .o4.o3.x      0  6 |  0   0 12 |  0   0   0  8 |  *   *   *   * 24 | 0  0  0  0  1 1
---------------+-------+-----------+---------------+-------------------+----------------
x.3o.4o.3o.     24  0 | 96   0  0 | 96   0   0  0 | 24   0   0   0  0 | 1  *  *  *  * *
xo3oo4oo ..&#x   6  1 | 12   6  0 |  8  12   0  0 |  1   8   0   0  0 | * 24  *  *  * *
xo3oo .. ox&#x   3  2 |  3   6  1 |  1   6   3  0 |  0   2   3   0  0 | *  * 96  *  * *
xo .. oo3ox&#x   2  3 |  1   6  3 |  0   3   6  1 |  0   0   3   2  0 | *  *  * 96  * *
.. oo4oo3ox&#x   1  6 |  0   6 12 |  0   0  12  8 |  0   0   0   8  1 | *  *  *  * 24 *
.o3.o4.o3.x      0 24 |  0   0 96 |  0   0   0 96 |  0   0   0   0 24 | *  *  *  *  * 1
or
o.3o.4o.3o.     & | 48    8   6 |  12  36 |  6  32  24 | 1  7  20
------------------+----+---------+---------+------------+---------
x. .. .. ..     & |  2 | 192   * |   3   3 |  3   6   3 | 1  3   4
oo3oo4oo3oo&#x    |  2 |   * 144    0   8 |  0   8   8 | 0  2   8
------------------+----+---------+---------+------------+---------
x.3o. .. ..     & |  3 |   3   0 | 192   * |  2   2   0 | 1  2   1
xo .. .. ..&#x  & |  3 |   1   2 |   * 576 |  0   2   2 | 0  1   3
------------------+----+---------+---------+------------+---------
x.3o.4o. ..     &   6 |  12   0 |   8   0 | 48   *   * | 1  1   0
xo3oo .. ..&#x  &   4 |   3   3 |   1   3 |  * 384   * | 0  1   1
xo .. .. ox&#x      4 |   2   4 |   0   4 |  *   * 288 | 0  0   2
------------------+----+---------+---------+------------+---------
x.3o.4o.3o.     &  24 |  96   0 |  96   0 | 24   0   0 | 2  *   *
xo3oo4oo ..&#x  &   7 |  12   6 |   8  12 |  1   8   0 | * 48   *
xo3oo .. ox&#x  &   5 |   4   6 |   1   9 |  0   2   3 | *  * 192

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