bitefa

Acronym bitefa

Name bitegmic hecatontetracontatetrachoron,
compound of 12 ico in spic army,
compound of 2 kitefa

Coxeter symbol 2{;3,4,3;}[12{3,4,3}]

Circumradius 1

©

General of army

spic

Embedding

o4o o4x o4o x4o x4x x4x x4o o4o o4w o4o x4x w4o w4o x4x o4x o4w q4q o4w o4x x4x w4o w4o x4x o4o o4w o4o x4o x4x x4x x4o o4o o4x o4o	hull = spic
o4o x4x o4o x4x q4q x4x o4o x4x o4o	vertex-inscribed non-uniform 2 ico compound, infact 6 such components then build this uniform compound. scaling factor = sqrt[2+sqrt(2)] = 1.847759 (vertex figure highlighted)
o4o x4o o4o x4o o4q x4o o4o x4o o4o	single ico component (display just slanted by 360°/16=22.5°)

Confer

blend-component:: ico
compounds:: kitefa

©

This compound occurs in different forms depending on whether the vertices (coincident by 2) will be counted separately (type A), or will be identified while the corealmic cells will still be counted separately (type C), or whether both would be unified (type E). All these would use 12 icositetrachora for compound components. – Two of those cases could be considered on base of the 6 icositetrachora compound (kitefa) instead, i.e. using just 2 such components. That then gives rise to (type B) with no identifications and (type D) with identification of vertices only. – As (type E) already cross-connects the octs of either kitefa, therefore there will be no according type using those for bases here. In fact, there are non-uniform compounds of 4 octs being used here. There is one central one plus three more, one each per axis, rotated half way. That whole cell is being displayed at the right.

How could this internal structure be understood? – The main idea to decipher the structure is to divide the vertex figure compound into 2 separate square prisms, which would just use a 2-square compound for base. Those bases for sure correspond to the 8-fold vertices of the right 4-oct compound. The 4 lateral faces of one of those cubes of the vertex figure then correspond to the only 4-fold vertices of the right compound cell. The 4 lateral faces of the other cube correspond to the remaining (normal) octs. The set of the triangles thus is to be divided too into subsets according to the adjoining cell types. Finally this requires a distinction of the edges as well, corresponding to the vertices of the 2 different cubes of the vertex figure.

Incidence matrix

(Type A) - no identifications

288 ♦    8 |   12 |   6 ||  1  verf: cube
----+------+------+-----++---
  2 | 1152 |    3 |   3 ||  1
----+------+------+-----++---
  3 |    3 | 1152 |   2 ||  1
----+------+------+-----++---
  6 |   12 |    8 | 288 ||  1  oct
----+------+------+-----++---
 24 |   96 |   96 |  24 || 12  ico

(Type B) - no identifications, but as 2 kitefa comp.

288 ♦    8 |   12 |   6 ||  1  verf: cube
----+------+------+-----++---
  2 | 1152 |    3 |   3 ||  1
----+------+------+-----++---
  3 |    3 | 1152 |   2 ||  1
----+------+------+-----++---
  6 |   12 |    8 | 288 ||  1  oct
----+------+------+-----++---
144 |  576 |  576 | 144 || 2  kitefa

(Type C) - identifying incident vertices only 

144 |   16 |   24 |  12 ||  2  verf: twirled face-first 2-cube comp. w/o identifications
----+------+------+-----++---
  2 | 1152 |    3 |   3 ||  1
----+------+------+-----++---
  3 |    3 | 1152 |   2 ||  1
----+------+------+-----++---
  6 |   12 |    8 | 288 ||  1  oct
----+------+------+-----++---
 24 |   96 |   96 |  24 || 12  ico

(Type D) - identifying incident vertices only, but as 2 kitefa comp.

144 |   16 |   24 |  12 || 2  verf: twirled face-first 2-cube comp. w/o identifications
----+------+------+-----++--
  2 | 1152 |    3 |   3 || 1
----+------+------+-----++--
  3 |    3 | 1152 |   2 || 1
----+------+------+-----++--
  6 |   12 |    8 | 288 || 1  oct
----+------+------+-----++--
144 |  576 |  576 | 144 || 2  kitefa

(Type E) - identifying vertices and corealmic cells

144 |   8   8 |  12   8   4 |  6  4 ||  2  verf: twirled face-first 2-cube comp. with coplanar faces unified as compound
----+---------+-------------+-------++---
  2 | 576   * |   3   0   0 |  3  0 ||  1
  2 |   * 576 |   0   2   1 |  1  2 ||  1
----+---------+-------------+-------++---
  3 |   3   0 | 576   *   * |  2  0 ||  1  faces of non-central oct of 4-oct
  3 |   0   3 |   * 384   * |  1  1 ||  1  faces of central oct of 4-oct
  3 |   0   3 |   *   * 192 |  0  2 ||  1
----+---------+-------------+-------++---
 18 |  36  12 |  24   8   0 | 48  * ||  4  4-oct compound
  6 |   0  12 |   0   4   4 |  * 96 ||  1  oct (in tet sym)
----+---------+-------------+-------++---
 24 |  48  48 |  48  32  16 |  4  8 || 12  ico

top of page