Acronym ...
Name lamina-truncate of hyperbolic x4x3o8o tesselation
Circumradius sqrt[-1/sqrt(8)] = 0.594604 i
Vertex figure oxo8ooo&#kt
Confer
uniform relative:
x4x3o8o  
general polytopal classes:
noble polytopes  

As the order 8 triangle tiling within x4x3o8o were hemi-choral (have same curvature resp. intersect the sphere of infinity orthogonally), those could be replaced by mirror images of the remainder each. This transforms the hypercompact honeycomb back into a compact one, a still uniform lamina-truncate, with tics only.


Incidence matrix according to Dynkin symbol

lamina-truncate( x4x3o8o )   (N → ∞)

. . . . | 3N |  2   8 | 16  8 | 16
--------+----+--------+-------+---
x . . . |  2 | 3N   * |  8  0 |  8
. x . . |  2 |  * 12N |  2  2 |  4
--------+----+--------+-------+---
x4x . . |  8 |  4   4 | 6N  * |  2
. x3o . |  3 |  0   3 |  * 8N |  2
--------+----+--------+-------+---
x4x3o .  24 | 12  24 |  6  8 | 2N

o8o3x4xØx4*c   (N → ∞)

. . . . .    | 6N |   8  1  1 |   8  8  8 |  8  8
-------------+----+-----------+-----------+------
. . x . .    |  2 | 24N  *  * |   2  1  1 |  2  2
. . . x .    |  2 |   * 3N  * |   0  8  0 |  8  0
. . . . x    |  2 |   *  * 3N |   0  0  8 |  0  8
-------------+----+-----------+-----------+------
. o3x . .    |  3 |   3  0  0 | 16N  *  * |  1  1
. . x4x .    |  8 |   4  4  0 |   * 6N  * |  2  0
. . x . x4*c |  8 |   4  0  4 |   *  * 6N |  0  2
-------------+----+-----------+-----------+------
. o3x4x .     24 |  24 12  0 |   8  6  0 | 2N  *
. o3x . x4*c  24 |  24  0 12 |   8  0  6 |  * 2N

© 2004-2024
top of page