Acronym idsrix
Name icositetra-diminished small rhombated hexacosachoron
Circumradius sqrt[19+8 sqrt(5)] = 6.073594
Dihedral angles
  • at {4} between co and pip:   arccos(-sqrt[(5+2 sqrt(5))/10]) = 166.717474°
  • at {3} between co and co:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between co and tricu:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between tricu and tricu:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {5} between id and pip:   162°
  • at {3} between co and id:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244°
  • at {3} between id and tricu:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244°
  • at {5} between id and ti:   144°
  • at {6} between ti and tricu:   arccos[-sqrt(5/8)] = 142.238756°
Confer
uniform relative:
sadi   srix  
related CRFs:
idprix   idsid pixhi   risadi   idsrahi  
segmentochora:
id || ti  

In the same way, as sadi was derived as an icositetrachoral diminishing of ex, idsrix can be derived as an icositetrachoral diminishing of srix. The fundamental domain of sadi (i.e. the dual of teddi), which there clearly encompasses just a single vertex, here would encompass a complete id. Therefore idsrix clearly is no longer uniform (as weren't lots of the Johnson solids neither).

Sadi was diminished at 24 vertices. Idsrix accordingly will be diminished at 24 ids. In fact 24 id-first caps will be chopped off. Any individual of those clearly is an id || ti. This results in several co, which get halved into tricu here.

Corresponding to the 3-fold symmetry of that domain we call the vertices of id as A, ..., G along its 3-fold axis. The other elements of idsrix then can be classified accordingly, as given below. The prime denotes equivalent elements, mirrored at a domain face which is close to A. The hash is the same with respect to a domain face which is close to G. The remaining domain face mirror images are denoted by an asterisk.


Incidence matrix

A       | 288   *   *   *   *   *   * |   2   2   0   0   0   0   0   0   0   0   0   0   2   0   0   0   0   0 |  1   1   0   0   0  0  1   0  0   2   2   0   0   0   0   2   0   0   0   0   0 |  1  1   2   0  1   0   0  0
B       |   * 576   *   *   *   *   * |   0   1   1   1   1   0   0   0   0   0   0   0   0   1   0   1   0   0 |  0   1   1   0   0  0  0   1  0   0   1   1   1   1   0   1   1   0   0   0   0 |  0  1   1   1  1   1   0  0
C       |   *   * 288   *   *   *   * |   0   0   0   2   0   2   0   0   0   0   0   0   0   0   1   0   0   0 |  0   0   2   0   0  0  0   0  0   0   0   0   2   0   0   1   0   1   0   2   0 |  0  0   1   0  1   2   0  1
D       |   *   *   * 576   *   *   * |   0   0   0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   0 |  0   0   1   1   0  0  0   0  0   0   0   0   0   1   1   0   1   1   0   1   1 |  0  0   0   1  1   1   1  1
E       |   *   *   *   * 288   *   * |   0   0   0   0   0   0   2   0   2   0   0   0   0   0   0   0   0   2 |  0   0   0   2   0  0  0   0  1   0   0   0   0   0   4   0   1   0   1   0   0 |  0  0   0   2  1   0   2  0
F       |   *   *   *   *   * 576   * |   0   0   0   0   0   0   0   1   1   1   1   0   0   0   0   0   1   0 |  0   0   0   1   1  0  0   0  0   0   0   0   0   1   1   0   0   1   1   1   1 |  0  0   0   1  1   1   1  1
G       |   *   *   *   *   *   * 288 |   0   0   0   0   0   0   0   0   0   0   2   2   0   0   0   2   0   0 |  0   0   0   0   1  1  0   1  0   0   0   2   0   2   0   0   0   0   2   0   0 |  0  1   0   2  1   1   0  0
--------+-----------------------------+-------------------------------------------------------------------------+---------------------------------------------------------------------------------+----------------------------
AA      |   2   0   0   0   0   0   0 | 288   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   * |  1   0   0   0   0  0  0   0  0   1   0   0   0   0   0   1   0   0   0   0   0 |  1  0   1   0  1   0   0  0
AB      |   1   1   0   0   0   0   0 |   * 576   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   * |  0   1   0   0   0  0  0   0  0   0   1   0   0   0   0   1   0   0   0   0   0 |  0  1   1   0  1   0   0  0
BB      |   0   2   0   0   0   0   0 |   *   * 288   *   *   *   *   *   *   *   *   *   *   *   *   *   *   * |  0   1   0   0   0  0  0   0  0   0   0   1   0   0   0   0   1   0   0   0   0 |  0  1   0   1  1   0   0  0
BC      |   0   1   1   0   0   0   0 |   *   *   * 576   *   *   *   *   *   *   *   *   *   *   *   *   *   * |  0   0   1   0   0  0  0   0  0   0   0   0   1   0   0   1   0   0   0   0   0 |  0  0   1   0  1   1   0  0
BD      |   0   1   0   1   0   0   0 |   *   *   *   * 576   *   *   *   *   *   *   *   *   *   *   *   *   * |  0   0   1   0   0  0  0   0  0   0   0   0   0   1   0   0   1   0   0   0   0 |  0  0   0   1  1   1   0  0
CD      |   0   0   1   1   0   0   0 |   *   *   *   *   * 576   *   *   *   *   *   *   *   *   *   *   *   * |  0   0   1   0   0  0  0   0  0   0   0   0   0   0   0   0   0   1   0   1   0 |  0  0   0   0  1   1   0  1
DE      |   0   0   0   1   1   0   0 |   *   *   *   *   *   * 576   *   *   *   *   *   *   *   *   *   *   * |  0   0   0   1   0  0  0   0  0   0   0   0   0   0   1   0   1   0   0   0   0 |  0  0   0   1  1   0   1  0
DF      |   0   0   0   1   0   1   0 |   *   *   *   *   *   *   * 576   *   *   *   *   *   *   *   *   *   * |  0   0   0   1   0  0  0   0  0   0   0   0   0   0   0   0   0   1   0   0   1 |  0  0   0   0  1   0   1  1
EF      |   0   0   0   0   1   1   0 |   *   *   *   *   *   *   *   * 576   *   *   *   *   *   *   *   *   * |  0   0   0   1   0  0  0   0  0   0   0   0   0   0   1   0   0   0   1   0   0 |  0  0   0   1  1   0   1  0
FF      |   0   0   0   0   0   2   0 |   *   *   *   *   *   *   *   *   * 288   *   *   *   *   *   *   *   * |  0   0   0   0   1  0  0   0  0   0   0   0   0   0   0   0   0   1   0   1   0 |  0  0   0   0  1   1   0  1
FG      |   0   0   0   0   0   1   1 |   *   *   *   *   *   *   *   *   *   * 576   *   *   *   *   *   *   * |  0   0   0   0   1  0  0   0  0   0   0   0   0   1   0   0   0   0   1   0   0 |  0  0   0   1  1   1   0  0
GG      |   0   0   0   0   0   0   2 |   *   *   *   *   *   *   *   *   *   *   * 288   *   *   *   *   *   * |  0   0   0   0   0  1  0   0  0   0   0   1   0   0   0   0   0   0   1   0   0 |  0  1   0   1  1   0   0  0
AA'     |   2   0   0   0   0   0   0 |   *   *   *   *   *   *   *   *   *   *   *   * 288   *   *   *   *   * |  0   0   0   0   0  0  1   0  0   1   1   0   0   0   0   0   0   0   0   0   0 |  1  1   1   0  0   0   0  0
BB'     |   0   2   0   0   0   0   0 |   *   *   *   *   *   *   *   *   *   *   *   *   * 288   *   *   *   * |  0   0   0   0   0  0  0   1  0   0   1   0   1   0   0   0   0   0   0   0   0 |  0  1   1   0  0   1   0  0
CC'     |   0   0   2   0   0   0   0 |   *   *   *   *   *   *   *   *   *   *   *   *   *   * 144   *   *   * |  0   0   0   0   0  0  0   0  0   0   0   0   2   0   0   0   0   0   0   2   0 |  0  0   1   0  0   2   0  1
BB*&GG# |   0   1   0   0   0   0   1 |   *   *   *   *   *   *   *   *   *   *   *   *   *   *   * 576   *   * |  0   0   0   0   0  0  0   1  0   0   0   1   0   1   0   0   0   0   0   0   0 |  0  1   0   1  0   1   0  0
DD*&FF# |   0   0   0   1   0   1   0 |   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   * 576   * |  0   0   0   0   0  0  0   0  0   0   0   0   0   1   1   0   0   0   0   1   1 |  0  0   0   1  0   1   1  1
EE*&EE# |   0   0   0   0   2   0   0 |   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   * 288 |  0   0   0   0   0  0  0   0  1   0   0   0   0   0   2   0   0   0   0   0   0 |  0  0   0   1  0   0   2  0
--------+-----------------------------+-------------------------------------------------------------------------+---------------------------------------------------------------------------------+----------------------------
AAA     |   3   0   0   0   0   0   0 |   3   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0 | 96   *   *   *   *  *  *   *  *   *   *   *   *   *   *   *   *   *   *   *   * |  1  0   0   0  1   0   0  0
ABB     |   1   2   0   0   0   0   0 |   0   2   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0 |  * 288   *   *   *  *  *   *  *   *   *   *   *   *   *   *   *   *   *   *   * |  0  1   0   0  1   0   0  0
BCD     |   0   1   1   1   0   0   0 |   0   0   0   1   1   1   0   0   0   0   0   0   0   0   0   0   0   0 |  *   * 576   *   *  *  *   *  *   *   *   *   *   *   *   *   *   *   *   *   * |  0  0   0   0  1   1   0  0
DEF     |   0   0   0   1   1   1   0 |   0   0   0   0   0   0   1   1   1   0   0   0   0   0   0   0   0   0 |  *   *   * 576   *  *  *   *  *   *   *   *   *   *   *   *   *   *   *   *   * |  0  0   0   0  1   0   1  0
FFG     |   0   0   0   0   0   2   1 |   0   0   0   0   0   0   0   0   0   1   2   0   0   0   0   0   0   0 |  *   *   *   * 288  *  *   *  *   *   *   *   *   *   *   *   *   *   *   *   * |  0  0   0   0  1   1   0  0
GGG     |   0   0   0   0   0   0   3 |   0   0   0   0   0   0   0   0   0   0   0   3   0   0   0   0   0   0 |  *   *   *   *   * 96  *   *  *   *   *   *   *   *   *   *   *   *   *   *   * |  0  1   0   0  1   0   0  0
A       |   3   0   0   0   0   0   0 |   0   0   0   0   0   0   0   0   0   0   0   0   3   0   0   0   0   0 |  *   *   *   *   *  * 96   *  *   *   *   *   *   *   *   *   *   *   *   *   * |  1  1   0   0  0   0   0  0
B&G     |   0   2   0   0   0   0   1 |   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   2   0   0 |  *   *   *   *   *  *  * 288  *   *   *   *   *   *   *   *   *   *   *   *   * |  0  1   0   0  0   1   0  0
E       |   0   0   0   0   3   0   0 |   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   3 |  *   *   *   *   *  *  *   * 96   *   *   *   *   *   *   *   *   *   *   *   * |  0  0   0   0  0   0   2  0
AA      |   4   0   0   0   0   0   0 |   2   0   0   0   0   0   0   0   0   0   0   0   2   0   0   0   0   0 |  *   *   *   *   *  *  *   *  * 144   *   *   *   *   *   *   *   *   *   *   * |  1  0   1   0  0   0   0  0
AB      |   2   2   0   0   0   0   0 |   0   2   0   0   0   0   0   0   0   0   0   0   1   1   0   0   0   0 |  *   *   *   *   *  *  *   *  *   * 288   *   *   *   *   *   *   *   *   *   * |  0  1   1   0  0   0   0  0
BB&GG   |   0   2   0   0   0   0   2 |   0   0   1   0   0   0   0   0   0   0   0   1   0   0   0   2   0   0 |  *   *   *   *   *  *  *   *  *   *   * 288   *   *   *   *   *   *   *   *   * |  0  1   0   1  0   0   0  0
BC      |   0   2   2   0   0   0   0 |   0   0   0   2   0   0   0   0   0   0   0   0   0   1   1   0   0   0 |  *   *   *   *   *  *  *   *  *   *   *   * 288   *   *   *   *   *   *   *   * |  0  0   1   0  0   1   0  0
BD&FG   |   0   1   0   1   0   1   1 |   0   0   0   0   1   0   0   0   0   0   1   0   0   0   0   1   1   0 |  *   *   *   *   *  *  *   *  *   *   *   *   * 576   *   *   *   *   *   *   * |  0  0   0   1  0   1   0  0
DE&EF   |   0   0   0   1   2   1   0 |   0   0   0   0   0   0   1   0   1   0   0   0   0   0   0   0   1   1 |  *   *   *   *   *  *  *   *  *   *   *   *   *   * 576   *   *   *   *   *   * |  0  0   0   1  0   0   1  0
ABC     |   2   2   1   0   0   0   0 |   1   2   0   2   0   0   0   0   0   0   0   0   0   0   0   0   0   0 |  *   *   *   *   *  *  *   *  *   *   *   *   *   *   * 288   *   *   *   *   * |  0  0   1   0  1   0   0  0
BDE     |   0   2   0   2   1   0   0 |   0   0   1   0   2   0   2   0   0   0   0   0   0   0   0   0   0   0 |  *   *   *   *   *  *  *   *  *   *   *   *   *   *   *   * 288   *   *   *   * |  0  0   0   1  1   0   0  0
CDF     |   0   0   1   2   0   2   0 |   0   0   0   0   0   2   0   2   0   1   0   0   0   0   0   0   0   0 |  *   *   *   *   *  *  *   *  *   *   *   *   *   *   *   *   * 288   *   *   * |  0  0   0   0  1   0   0  1
EFG     |   0   0   0   0   1   2   2 |   0   0   0   0   0   0   0   0   2   0   2   1   0   0   0   0   0   0 |  *   *   *   *   *  *  *   *  *   *   *   *   *   *   *   *   *   * 288   *   * |  0  0   0   1  1   0   0  0
CD&FF   |   0   0   2   2   0   2   0 |   0   0   0   0   0   2   0   0   0   1   0   0   0   0   1   0   2   0 |  *   *   *   *   *  *  *   *  *   *   *   *   *   *   *   *   *   *   * 288   * |  0  0   0   0  0   1   0  1
DF      |   0   0   0   3   0   3   0 |   0   0   0   0   0   0   0   3   0   0   0   0   0   0   0   0   3   0 |  *   *   *   *   *  *  *   *  *   *   *   *   *   *   *   *   *   *   *   * 192 |  0  0   0   0  0   0   1  1
--------+-----------------------------+-------------------------------------------------------------------------+---------------------------------------------------------------------------------+----------------------------
AAA       12   0   0   0   0   0   0 |  12   0   0   0   0   0   0   0   0   0   0   0  12   0   0   0   0   0 |  4   0   0   0   0  0  4   0  0   6   0   0   0   0   0   0   0   0   0   0   0 | 24  *   *   *  *   *   *  *
ABB&GGG    3   6   0   0   0   0   3 |   0   6   3   0   0   0   0   0   0   0   0   3   3   3   0   6   0   0 |  0   3   0   0   0  1  1   3  0   0   3   3   0   0   0   0   0   0   0   0   0 |  * 96   *   *  *   *   *  *
ABC        4   4   2   0   0   0   0 |   2   4   0   4   0   0   0   0   0   0   0   0   2   2   1   0   0   0 |  0   0   0   0   0  0  0   0  0   1   2   0   2   0   0   2   0   0   0   0   0 |  *  * 144   *  *   *   *  *
BDE&EFG    0   2   0   2   2   2   2 |   0   0   1   0   2   0   2   0   2   0   2   1   0   0   0   2   2   1 |  0   0   0   0   0  0  0   0  0   0   0   1   0   2   2   0   1   0   1   0   0 |  *  *   * 288  *   *   *  *
id         3   6   3   6   3   6   3 |   3   6   3   6   6   6   6   6   6   3   6   3   0   0   0   0   0   0 |  1   3   6   6   3  1  0   0  0   0   0   0   0   0   0   3   3   3   3   0   0 |  *  *   *   * 96   *   *  *
BCD&FFG    0   2   2   2   0   2   1 |   0   0   0   2   2   2   0   0   0   1   2   0   0   1   1   2   2   0 |  0   0   2   0   1  0  0   1  0   0   0   0   1   2   0   0   0   0   0   1   0 |  *  *   *   *  * 288   *  *
DEF        0   0   0   3   3   3   0 |   0   0   0   0   0   0   3   3   3   0   0   0   0   0   0   0   3   3 |  0   0   0   3   0  0  0   0  1   0   0   0   0   0   3   0   0   0   0   0   1 |  *  *   *   *  *   * 192  *
ti         0   0  12  24   0  24   0 |   0   0   0   0   0  24   0  24   0  12   0   0   0   0   6   0  24   0 |  0   0   0   0   0  0  0   0  0   0   0   0   0   0   0   0   0  12   0  12   8 |  *  *   *   *  *   *   * 24

© 2004-2018
top of page