Acronym ...
Name hyperbolic x3x4x3x8o tesselation
Circumradius sqrt[-(4+7 sqrt(2))]/2 = 1.864101 i
Confer
uniform relative:
lamina-trunc( x3x4x3x8o )  

This hypercompact hyperbolic tesselation uses the truncated order 8 triangle tiling (totrat) in the sense of an infinite bollohedron as one of its cell types. Further it uses x x3x8o and x4x3x8o in the sense of infinite bollochora alike.

As the latter of 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( x3x4x3x8o )).


Incidence matrix according to Dynkin symbol

x3x4x3x8o   (N,M,K → ∞)

. . . . . | 576NMK |      1      1      1      2 |     1      1      2     1      2      2     1 |     1     2     2     1     2     1    1 |   2     1    1    1
----------+--------+-----------------------------+-----------------------------------------------+------------------------------------------+--------------------
x . . . . |      2 | 288NMK      *      *      * |     1      1      2     0      0      0     0 |     1     2     2     1     0     0    0 |   2     1    1    0
. x . . . |      2 |      * 288NMK      *      * |     1      0      0     1      2      0     0 |     1     2     0     0     2     1    0 |   2     1    0    1
. . x . . |      2 |      *      * 288NMK      * |     0      1      0     1      0      2     0 |     1     0     2     0     2     0    1 |   2     0    1    1
. . . x . |      2 |      *      *      * 576NMK |     0      0      1     0      1      1     1 |     0     1     1     1     1     1    1 |   1     1    1    1
----------+--------+-----------------------------+-----------------------------------------------+------------------------------------------+--------------------
x3x . . . |      6 |      3      3      0      0 | 96NMK      *      *     *      *      *     * |     1     2     0     0     0     0    0 |   2     1    0    0
x . x . . |      4 |      2      0      2      0 |     * 144NMK      *     *      *      *     * |     1     0     2     0     0     0    0 |   2     0    1    0
x . . x . |      4 |      2      0      0      2 |     *      * 288NMK     *      *      *     * |     0     1     1     1     0     0    0 |   1     1    1    0
. x4x . . |      8 |      0      4      4      0 |     *      *      * 72NMK      *      *     * |     1     0     0     0     2     0    0 |   2     0    0    1
. x . x . |      4 |      0      2      0      2 |     *      *      *     * 288NMK      *     * |     0     1     0     0     1     1    0 |   1     1    0    1
. . x3x . |      6 |      0      0      3      3 |     *      *      *     *      * 192NMK     * |     0     0     1     0     1     0    1 |   1     0    1    1
. . . x8o |      8 |      0      0      0      8 |     *      *      *     *      *      * 72NMK |     0     0     0     1     0     1    1 |   0     1    1    1
----------+--------+-----------------------------+-----------------------------------------------+------------------------------------------+--------------------
x3x4x . .      48 |     24     24     24      0 |     8     12      0     6      0      0     0 | 12NMK     *     *     *     *     *    * |   2     0    0    0
x3x . x .      12 |      6      6      0      6 |     2      0      3     0      3      0     0 |     * 96NMK     *     *     *     *    * |   1     1    0    0
x . x3x .      12 |      6      0      6      6 |     0      3      3     0      0      2     0 |     *     * 96NMK     *     *     *    * |   1     0    1    0
x . . x8o      16 |      8      0      0     16 |     0      0      8     0      0      0     2 |     *     *     * 36NMK     *     *    * |   0     1    1    0
. x4x3x .      48 |      0     24     24     24 |     0      0      0     6     12      8     0 |     *     *     *     * 24NMK     *    * |   1     0    0    1
. x . x8o      16 |      0      8      0     16 |     0      0      0     0      8      0     2 |     *     *     *     *     * 36NMK    * |   0     1    0    1
. . x3x8o     24M |      0      0    12M    24M |     0      0      0     0      0     8M    3M |     *     *     *     *     *     * 24NK |   0     0    1    1
----------+--------+-----------------------------+-----------------------------------------------+------------------------------------------+--------------------
x3x4x3x .    1152 |    576    576    576    576 |   192    288    288   144    288    192     0 |    24    96    96     0    24     0    0 | NMK     *    *    *
x3x . x8o      48 |     24     24      0     48 |     8      0     24     0     24      0     6 |     0     8     0     3     0     3    0 |   * 12NMK    *    *
x . x3x8o     48M |    24M      0    24M    48M |     0    12M    24M     0      0    16M    6M |     0     0    8M    3M     0     0    2 |   *     * 12NK    *
. x4x3x8o    48MK |      0   24MK   24MK   48MK |     0      0      0   6MK   24MK   16MK   6MK |     0     0     0     0   2MK   3MK   2K |   *     *    * 12NM

© 2004-2021
top of page