Acronym bamic (old: apic)
Name biambotetracontoctachoron,
antiprismatotetracontoctachoron,
triangle based biambotetracontoctachoron
 
 ©
Circumradius sqrt(3) = 1.732051
Confer
general polytopal classes:
isogonal  
External
links
polytopewiki  

Rectification, when applicable, results in using a specific point on each edge. Ambification simplifies that by using the midpoint always. Birectification, when applicable, results in using a specific point on each face. Biambification accordingly simplifies that by using the respective centerpoint. But the tetracontoctachoron uses 2 types of faces, whereas only the trigonal ones do contribute, while the octagonal ones do not contribute in these isogonal polychoron. (In fact, else it won't be isogonal any more.)

Note that the similar hull of the centers of the octagons of cont would simply reproduce the topology of spic: each tic provides an inscribed oct, then in expanded position.


Incidence matrix according to Dynkin symbol

oo3xo4ox3oo&#zy   → height = 0
                    y = 2-sqrt(2) = 0.585786
(tegum sum of 2 inverted ricos)

o.3o.4o.3o.    | 96  * |   6   3   0 |   6   6   3   0 |  2   6  0
.o3.o4.o3.o    |  * 96 |   0   3   6 |   0   3   6   6 |  0   6  2
---------------+-------+-------------+-----------------+----------
.. x. .. ..    |  2  0 | 288   *   * |   2   1   0   0 |  1   2  0
oo3oo4oo3oo&#y |  1  1 |   * 288   * |   0   2   2   0 |  0   4  0
.. .. .x ..    |  0  2 |   *   * 288 |   0   0   1   2 |  0   2  1
---------------+-------+-------------+-----------------+----------
.. x.4o. ..    |  4  0 |   4   0   0 | 144   *   *   * |  1   1  0
.. xo .. ..&#y |  2  1 |   1   2   0 |   * 288   *   * |  0   2  0
.. .. ox ..&#y |  1  2 |   0   2   1 |   *   * 288   * |  0   2  0
.. .o4.x ..    |  0  4 |   0   0   4 |   *   *   * 144 |  0   1  1
---------------+-------+-------------+-----------------+----------
.. x.4o.3o.    |  8  0 |  12   0   0 |   6   0   0   0 | 24   *  *  cube
.. xo4ox ..&#y |  4  4 |   4   8   4 |   1   4   4   1 |  * 144  *  (x,y)-4ap
.o3.o4.x ..    |  0  8 |   0   0  12 |   0   0   0   6 |  *   * 24  cube
or
o.3o.4o.3o.    & | 192 |   6   3 |   6   9 |  2   6
-----------------+-----+---------+---------+-------
.. x. .. ..    & |   2 | 576   * |   2   1 |  1   2
oo3oo4oo3oo&#y   |   2 |   * 288 |   0   4 |  0   4
-----------------+-----+---------+---------+-------
.. x.4o. ..    & |   4 |   4   0 | 288   * |  1   1
.. xo .. ..&#y & |   3 |   1   2 |   * 576 |  0   2
-----------------+-----+---------+---------+-------
.. x.4o.3o.    & |   8 |  12   0 |   6   0 | 48   *  cube
.. xo4ox ..&#y   |   8 |   8   8 |   2   8 |  * 144  (x,y)-4ap

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