Acronym ...
Name hyperbolic x4x4o5o tesselation
 
 ©
Circumradius sqrt[(10 sqrt(5)-121)/190] = 0.720524 i

This hypercompact hyperbolic tesselation uses tosquat and pesquat in the sense of an infinite holohedron and bollohedron respectively as its cell types.

This non-compact hyperbolic tesselation is of level 2, as it requires the deletion of any 2 nodes of its diagramm in order to get the remaining components are all finite or affine each. Accordingly it has a honeycomb inside the space, and sphere packing on the boundary, as can be seen in the above picture.


Incidence matrix according to Dynkin symbol

x4x4o5o   (N,M,K,L → ∞)

. . . . | 8NMK |     1      5 |     5      5 |     5    1
--------+------+--------------+--------------+-----------
x . . . |    2 | 4NMKL      * |     5      0 |     5    0  (gold)
. x . . |    2 |     * 20NMKL |     1      2 |     2    1  (silver)
--------+------+--------------+--------------+-----------
x4x . . |    8 |     4      4 | 5NMKL      * |     2    0
. x4o . |    4 |     0      4 |     * 10NMKL |     1    1
--------+------+--------------+--------------+-----------
x4x4o .    4M |    2M     4M |     M      M | 10NKL    *
. x4o5o    4K |     0    10K |     0     5K |     * 2NML

© 2004-2024
top of page