Acronym ...
Name rectified Shephard's tesseract,
complex polychoron op-4-x2-3-o2-3-o2
Coordinates (εpn, εpm, εpk, 0)   & all permutations, each for any 1≤n,m,k≤p, where εp=exp(2πi/p)
Face vector 4p3, 6p4, 2p2(2p2+3), p(p3+4)
Confer
general polytopal classes:
complex polytopes  

This is the rectification of Shephard's tesseract. Accordingly it re-uses the edge count of its pre-image as its new vertex count. The new edge type will be 2-fold, i.e. are real ones only. It will have 2 complex face types, the first being the duals of the ones of its pre-image (which here are op-4-x2), the others are the faces of the former's vertex figure (real space triangles). There are 2 complex cell types too, the first being rectified Shephard's cubes, the others are the former's vertex figures, i.e. (real space) tets. The new vertex figures in here are the complex reducible polyhedra yp   x2-3-o2 (for some, here so far not yet further analysed edge size y).


Incidence matrix according to Dynkin symbol

op-4-x2-3-o2-3-o2

.    .    .    .  | 4p3 ♦ 3p  |  3  3p  |  3 p 
-----------------+-----+-----+---------+------
.    x2   .    .  |  2  | 6p4 |  1   2  |  2 1 
-----------------+-----+-----+---------+------
op-4-x2   .    .  ♦ 2p  |  p2 | 6p2  *  |  2 0 
.    x2-3-o2   .  |  3  |  3  |  *  4p4 |  1 1 
-----------------+-----+-----+---------+------
op-4-x2-3-o2   .  ♦ 3p2 | 3p3 | 3p   p3 | 4p * 
.    x2-3-o2-3-o2 ♦  4  |  6  |  0   4  |  * p4

© 2004-2024
top of page