It is quite remarkable that icoap allows for some of the same operations as regulars do: This polyteron is nothing but the ambification operation being applied to it. However, its outcome is still both CRF and orbiform.

Incidence matrix according to symbol extension

ambo(  xo3oo4oo3ox&#x )

mids(  x. .. .. ..    ) & | 192   * |   6    6   0 |   3   3   6   12   0    6 |  3   6   3  2   6  0   6   2 | 1  3   4  2
mids(  oo3oo4oo3oo&#x )   |   * 144 |   0    8   8 |   0   8   0    8   8   16 |  0   8   8  0   2  2   8   8 | 0  2   8  2
--------------------------+---------+--------------+---------------------------+------------------------------+------------
verf(  x.3o. .. ..    ) & |   2   0 | 576    *   * |   1   0   2    2   0    0 |  2   2   0  1   2  0   1   0 | 1  2   1  1
verfA( xo .. .. ..&#x ) & |   1   1 |   * 1152   * |   0   1   0    2   0    2 |  0   2   2  0   1  0   2   1 | 0  1   3  1
verfB( xo .. .. ..&#x ) & |   0   2 |   *    * 576 |   0   1   0    0   2    2 |  0   2   2  0   0  1   1   2 | 0  1   3  1
--------------------------+---------+--------------+---------------------------+------------------------------+------------
ambo(  x.3o. .. ..    ) & |   3   0 |   3    0   0 | 192   *   *    *   *    * |  2   2   0  0   0  0   0   0 | 1  2   1  0
ambo(  xo .. .. ..    ) & |   1   2 |   0    2   1 |   * 576   *    *   *    * |  0   2   2  0   0  0   0   0 | 0  1   3  0
verf(  x.3o.4o. ..    ) & |   4   0 |   4    0   0 |   *   * 288    *   *    * |  1   0   0  1   1  0   0   0 | 1  1   0  1
verfA( xo3oo .. ..&#x ) & |   2   1 |   1    2   0 |   *   *   * 1152   *    * |  0   1   0  0   1  0   1   0 | 0  1   1  1
verfB( xo3oo .. ..&#x ) & |   0   3 |   0    0   3 |   *   *   *    * 384    * |  0   1   0  0   0  1   0   1 | 0  1   1  1
verf(  xo .. .. ox&#x )   |   1   2 |   0    2   1 |   *   *   *    *   * 1152 |  0   0   1  0   0  0   1   1 | 0  0   2  1
--------------------------+---------+--------------+---------------------------+------------------------------+------------
ambo(  x.3o.4o. ..    ) & ♦  12   0 |  24    0   0 |   8   0   6    0   0    0 | 48   *   *  *   *  *   *   * | 1  1   0  0
ambo(  xo3oo .. ..&#x ) & ♦   3   3 |   3    6   3 |   1   3   0    3   1    0 |  * 384   *  *   *  *   *   * | 0  1   1  0
ambo(  xo .. .. ox&#x )   ♦   2   4 |   0    8   4 |   0   4   0    0   0    4 |  *   * 288  *   *  *   *   * | 0  0   2  0
verf(  x.3o.4o.3o.    ) & ♦   8   0 |  12    0   0 |   0   0   6    0   0    0 |  *   *   * 48   *  *   *   * | 1  0   0  1
verfA( xo3oo4oo ..&#x ) & ♦   4   1 |   4    4   0 |   0   0   1    4   0    0 |  *   *   *  * 288  *   *   * | 0  1   0  1
verfB( xo3oo4oo ..&#x ) & ♦   0   6 |   0    0  12 |   0   0   0    0   8    0 |  *   *   *  *   * 48   *   * | 0  1   0  1
verfA( xo3oo .. ox&#x ) & ♦   2   2 |   1    4   1 |   0   0   0    2   0    2 |  *   *   *  *   *  * 576   * | 0  0   1  1
verfB( xo3oo .. ox&#x ) & ♦   1   3 |   0    3   3 |   0   0   0    0   1    3 |  *   *   *  *   *  *   * 384 | 0  0   1  1
--------------------------+---------+--------------+---------------------------+------------------------------+------------
ambo(  x.3o.4o.3o.    ) & ♦  96   0 | 288    0   0 |  96   0 144    0   0    0 | 24   0   0 24   0  0   0   0 | 2  *   *  *
ambo(  xo3oo4oo ..&#x ) & ♦  12   6 |  24   24  12 |   8  12   6   24   8    0 |  1   8   0  0   6  1   0   0 | * 48   *  *
ambo(  xo3oo .. ox&#x ) & ♦   4   6 |   3   18   9 |   1   9   0    6   2   12 |  0   2   3  0   0  0   3   2 | *  * 192  *
verf(  xo3oo4oo3ox&#x )   ♦   8   6 |  12   24  12 |   0   0   6   24   8   24 |  0   0   0  1   6  1  12   8 | *  *   * 48

oxo3xoo4oox3oxo&#xt   → both heights = sqrt[sqrt(2)-1] = 0.643594
(rico || pseudo spic || inv rico)

o..3o..4o..3o..     | 96   *  * |   6   6   0   0   0   0 |  3   6   3  12   6   0   0   0   0   0   0  0 |  3  2   6   3   6   6   2  0  0   0   0   0   0  0  0 | 1  3  3  1  2  0  0 0
.o.3.o.4.o.3.o.     |  * 144  * |   0   4   4   4   4   0 |  0   0   4   4   8   4   4   8   4   4   0  0 |  0  0   4   8   1   4   4  1  1   4   4   1   4  0  0 | 0  1  4  4  1  1  1 0
..o3..o4..o3..o     |  *   * 96 |   0   0   0   0   6   6 |  0   0   0   0   0   0   0   6  12   3   6  3 |  0  0   0   3   0   0   0  0  0   2   6   6   6  2  3 | 0  0  1  3  0  2  3 1
--------------------+-----------+-------------------------+-----------------------------------------------+-------------------------------------------------------+----------------------
... x.. ... ...     |  2   0  0 | 288   *   *   *   *   * |  1   2   0   2   0   0   0   0   0   0   0  0 |  2  1   2   0   2   1   0  0  0   0   0   0   0  0  0 | 1  2  1  0  1  0  0 0
oo.3oo.4oo.3oo.&#x  |  1   1  0 |   * 576   *   *   *   * |  0   0   1   2   2   0   0   0   0   0   0  0 |  0  0   2   2   1   2   1  0  0   0   0   0   0  0  0 | 0  1  2  1  1  0  0 0
.x. ... ... ...     |  0   2  0 |   *   * 288   *   *   * |  0   0   1   0   0   2   0   2   0   0   0  0 |  0  0   2   2   0   0   0  1  0   2   1   0   0  0  0 | 0  1  2  1  0  1  0 0
... ... ... .x.     |  0   2  0 |   *   *   * 288   *   * |  0   0   0   0   2   0   2   0   0   1   0  0 |  0  0   0   2   0   1   2  0  1   0   0   0   2  0  0 | 0  0  1  2  1  0  1 0
.oo3.oo4.oo3.oo&#x  |  0   1  1 |   *   *   *   * 576   * |  0   0   0   0   0   0   0   2   2   1   0  0 |  0  0   0   2   0   0   0  0  0   1   2   1   2  0  0 | 0  0  1  2  0  1  1 0
... ... ..x ...     |  0   0  2 |   *   *   *   *   * 288 |  0   0   0   0   0   0   0   0   2   0   2  1 |  0  0   0   0   0   0   0  0  0   0   1   2   2  1  2 | 0  0  0  1  0  1  2 1
--------------------+-----------+-------------------------+-----------------------------------------------+-------------------------------------------------------+----------------------
o..3x.. ... ...     |  3   0  0 |   3   0   0   0   0   0 | 96   *   *   *   *   *   *   *   *   *   *  * |  2  0   2   0   0   0   0  0  0   0   0   0   0  0  0 | 1  2  1  0  0  0  0 0
... x..4o.. ...     |  4   0  0 |   4   0   0   0   0   0 |  * 144   *   *   *   *   *   *   *   *   *  * |  1  1   0   0   1   0   0  0  0   0   0   0   0  0  0 | 1  1  0  0  1  0  0 0
ox. ... ... ...&#x  |  1   2  0 |   0   2   1   0   0   0 |  *   * 288   *   *   *   *   *   *   *   *  * |  0  0   2   2   0   0   0  0  0   0   0   0   0  0  0 | 0  1  2  1  0  0  0 0
... xo. ... ...&#x  |  2   1  0 |   1   2   0   0   0   0 |  *   *   * 576   *   *   *   *   *   *   *  * |  0  0   1   0   1   1   0  0  0   0   0   0   0  0  0 | 0  1  1  0  1  0  0 0
... ... ... ox.&#x  |  1   2  0 |   0   2   0   1   0   0 |  *   *   *   * 576   *   *   *   *   *   *  * |  0  0   0   1   0   1   1  0  0   0   0   0   0  0  0 | 0  0  1  1  1  0  0 0
.x.3.o. ... ...     |  0   3  0 |   0   0   3   0   0   0 |  *   *   *   *   * 192   *   *   *   *   *  * |  0  0   1   0   0   0   0  1  0   1   0   0   0  0  0 | 0  1  1  0  0  1  0 0
... ... .o.3.x.     |  0   3  0 |   0   0   0   3   0   0 |  *   *   *   *   *   * 192   *   *   *   *  * |  0  0   0   0   0   0   1  0  1   0   0   0   1  0  0 | 0  0  0  1  1  0  1 0
.xo ... ... ...&#x  |  0   2  1 |   0   0   1   0   2   0 |  *   *   *   *   *   *   * 576   *   *   *  * |  0  0   0   1   0   0   0  0  0   1   1   0   0  0  0 | 0  0  1  1  0  1  0 0
... ... .ox ...&#x  |  0   1  2 |   0   0   0   0   2   1 |  *   *   *   *   *   *   *   * 576   *   *  * |  0  0   0   0   0   0   0  0  0   0   1   1   1  0  0 | 0  0  0  1  0  1  1 0
... ... ... .xo&#x  |  0   2  1 |   0   0   0   1   2   0 |  *   *   *   *   *   *   *   *   * 288   *  * |  0  0   0   2   0   0   0  0  0   0   0   0   2  0  0 | 0  0  1  2  0  0  1 0
... ..o4..x ...     |  0   0  4 |   0   0   0   0   0   4 |  *   *   *   *   *   *   *   *   *   * 144  * |  0  0   0   0   0   0   0  0  0   0   0   1   0  1  1 | 0  0  0  0  0  1  1 1
... ... ..x3..o     |  0   0  3 |   0   0   0   0   0   3 |  *   *   *   *   *   *   *   *   *   *   * 96 |  0  0   0   0   0   0   0  0  0   0   0   0   2  0  2 | 0  0  0  1  0  0  2 1
--------------------+-----------+-------------------------+-----------------------------------------------+-------------------------------------------------------+----------------------
o..3x..4o.. ...     ♦ 12   0  0 |  24   0   0   0   0   0 |  8   6   0   0   0   0   0   0   0   0   0  0 | 24  *   *   *   *   *   *  *  *   *   *   *   *  *  * | 1  1  0  0  0  0  0 0
... x..4o..3o..     ♦  8   0  0 |  12   0   0   0   0   0 |  0   6   0   0   0   0   0   0   0   0   0  0 |  * 24   *   *   *   *   *  *  *   *   *   *   *  *  * | 1  0  0  0  1  0  0 0
ox.3xo. ... ...&#x  ♦  3   3  0 |   3   6   3   0   0   0 |  1   0   3   3   0   1   0   0   0   0   0  0 |  *  * 192   *   *   *   *  *  *   *   *   *   *  *  * | 0  1  1  0  0  0  0 0
oxo ... ... oxo&#xt ♦  1   4  1 |   0   4   2   2   4   0 |  0   0   2   0   2   0   0   2   0   2   0  0 |  *  *   * 288   *   *   *  *  *   *   *   *   *  *  * | 0  0  1  1  0  0  0 0
... xo.4oo. ...&#x  ♦  4   1  0 |   4   4   0   0   0   0 |  0   1   0   4   0   0   0   0   0   0   0  0 |  *  *   *   * 144   *   *  *  *   *   *   *   *  *  * | 0  1  0  0  1  0  0 0
... xo. ... ox.&#x  ♦  2   2  0 |   1   4   0   1   0   0 |  0   0   0   2   2   0   0   0   0   0   0  0 |  *  *   *   *   * 288   *  *  *   *   *   *   *  *  * | 0  0  1  0  1  0  0 0
... ... oo.3ox.&#x  ♦  1   3  0 |   0   3   0   3   0   0 |  0   0   0   0   3   0   1   0   0   0   0  0 |  *  *   *   *   *   * 192  *  *   *   *   *   *  *  * | 0  0  0  1  1  0  0 0
.x.3.o.4.o. ...     ♦  0   6  0 |   0   0  12   0   0   0 |  0   0   0   0   0   8   0   0   0   0   0  0 |  *  *   *   *   *   *   * 24  *   *   *   *   *  *  * | 0  1  0  0  0  1  0 0
... .o.4.o.3.x.     ♦  0   6  0 |   0   0   0  12   0   0 |  0   0   0   0   0   0   8   0   0   0   0  0 |  *  *   *   *   *   *   *  * 24   *   *   *   *  *  * | 0  0  0  0  1  0  1 0
.xo3.oo ... ...&#x  ♦  0   3  1 |   0   0   3   0   3   0 |  0   0   0   0   0   1   0   3   0   0   0  0 |  *  *   *   *   *   *   *  *  * 192   *   *   *  *  * | 0  0  1  0  0  1  0 0
.xo ... .ox ...&#x  ♦  0   2  2 |   0   0   1   0   4   1 |  0   0   0   0   0   0   0   2   2   0   0  0 |  *  *   *   *   *   *   *  *  *   * 288   *   *  *  * | 0  0  0  1  0  1  0 0
... .oo4.ox ...&#x  ♦  0   1  4 |   0   0   0   0   4   4 |  0   0   0   0   0   0   0   0   4   0   1  0 |  *  *   *   *   *   *   *  *  *   *   * 144   *  *  * | 0  0  0  0  0  1  1 0
... ... .ox3.xo&#x  ♦  0   3  3 |   0   0   0   3   6   3 |  0   0   0   0   0   0   1   0   3   3   0  1 |  *  *   *   *   *   *   *  *  *   *   *   * 192  *  * | 0  0  0  1  0  0  1 0
..o3..o4..x ...     ♦  0   0  8 |   0   0   0   0   0  12 |  0   0   0   0   0   0   0   0   0   0   6  0 |  *  *   *   *   *   *   *  *  *   *   *   *   * 24  * | 0  0  0  0  0  1  0 1
... ..o4..x3..o     ♦  0   0 12 |   0   0   0   0   0  24 |  0   0   0   0   0   0   0   0   0   0   6  8 |  *  *   *   *   *   *   *  *  *   *   *   *   *  * 24 | 0  0  0  0  0  0  1 1
--------------------+-----------+-------------------------+-----------------------------------------------+-------------------------------------------------------+----------------------
o..3x..4o..3o..     ♦ 96   0  0 | 288   0   0   0   0   0 | 96 144   0   0   0   0   0   0   0   0   0  0 | 24 24   0   0   0   0   0  0  0   0   0   0   0  0  0 | 1  *  *  *  *  *  * *
ox.3xo.4oo. ...&#x  ♦ 12   6  0 |  24  24  12   0   0   0 |  8   6  12  24   0   8   0   0   0   0   0  0 |  1  0   8   0   6   0   0  1  0   0   0   0   0  0  0 | * 24  *  *  *  *  * *
oxo3xoo ... oxo&#xt ♦  3   6  1 |   3  12   6   3   6   0 |  1   0   6   6   6   2   0   6   0   3   0  0 |  0  0   2   3   0   3   0  0  0   2   0   0   0  0  0 | *  * 96  *  *  *  * *
oxo ... oox3oxo&#xt ♦  1   6  3 |   0   6   3   6  12   3 |  0   0   3   0   6   0   2   6   6   6   0  1 |  0  0   0   3   0   0   2  0  0   0   3   0   2  0  0 | *  *  * 96  *  *  * *
... xo.4oo.3ox.&#x  ♦  8   6  0 |  12  24   0  12   0   0 |  0   6   0  24  24   0   8   0   0   0   0  0 |  0  1   0   0   6  12   8  0  1   0   0   0   0  0  0 | *  *  *  * 24  *  * *
.xo3.oo4.ox ...&#x  ♦  0   6  8 |   0   0  12   0  24  12 |  0   0   0   0   0   8   0  24  24   0   6  0 |  0  0   0   0   0   0   0  1  0   8  12   6   0  1  0 | *  *  *  *  * 24  * *
... .oo4.ox3.xo&#x  ♦  0   6 12 |   0   0   0  12  24  24 |  0   0   0   0   0   0   8   0  24  12   6  8 |  0  0   0   0   0   0   0  0  1   0   0   6   8  0  1 | *  *  *  *  *  * 24 *
..o3..o4..x3..o     ♦  0   0 96 |   0   0   0   0   0 288 |  0   0   0   0   0   0   0   0   0   0 144 96 |  0  0   0   0   0   0   0  0  0   0   0   0   0 24 24 | *  *  *  *  *  *  * 1