Acronym ...
Name hyperbolic o3x4x3o8o tesselation
Circumradius sqrt[-1/sqrt(8)] = 0.594604 i
Confer
uniform relative:
lamina-trunc( o3x4x3o8o )  

This hypercompact hyperbolic tesselation uses the order 8 triangle tiling (otrat) in the sense of an infinite bollohedron as one of its cell types. Further it uses x4x3o8o in the sense of an infinite bollochoron alike.

As these very bollochora are hemi-teral (have same curvature resp. intersect the hypersphere of infinity orthogonally) those could be replaced by mirror images of the remainder each. This transforms the hypercompact tetracomb back into a compact one, into lamina-trunc( o3x4x3o8o ) (contit).


Incidence matrix according to Dynkin symbol

o3x4x3o8o   (N,M,K → ∞)

. . . . . | 36NMK |     2      8 |     1    16     8 |     8    16    1 |   8   2
----------+-------+--------------+-------------------+------------------+--------
. x . . . |     2 | 36NMK      * |     1     8     0 |     8     8    0 |   8   1
. . x . . |     2 |     * 144NMK |     0     2     2 |     1     4    1 |   2   2
----------+-------+--------------+-------------------+------------------+--------
o3x . . . |     3 |     3      0 | 12NMK     *     * |     8     0    0 |   8   0
. x4x . . |     8 |     4      4 |     * 72NMK     * |     1     2    0 |   2   1
. . x3o . |     3 |     0      3 |     *     * 96NMK |     0     2    1 |   1   2
----------+-------+--------------+-------------------+------------------+--------
o3x4x . .     24 |    24     12 |     8     6     0 | 12NMK     *    * |   2   0
. x4x3o .     24 |    12     24 |     0     6     8 |     * 24NMK    * |   1   1
. . x3o8o     3M |     0    12M |     0     0    8M |     *     * 12NK |   0   2
----------+-------+--------------+-------------------+------------------+--------
o3x4x3o .    288 |   288    288 |    96   144    96 |    24    24    0 | NMK   *
. x4x3o8o    6MK |   3MK   24MK |     0   6MK  16MK |     0   2MK   2K |   * 12N

© 2004-2021
top of page