Acronym bitdi
Name chiral Weimholt hexahedron,
bitrigonally diminished icosahedron,
vertex figure of bidex
 
    ©
Circumradius sqrt[(5+sqrt(5))/8] = 0.951057
Vertex figures ovo&#(v,x)t, of&#x
Dual selfdual
Dihedral angles
  • at f-edges like doe:   arccos(-1/sqrt(5)) = 116.565051°
  • at x-edges like gad:   arccos(1/sqrt(5)) = 63.434949°
Confer
related Johnson solids:
peppy   teddi  
uniform relative:
ike  
related CRF:
bidex  
general polytopal classes:
subsymmetrical diminishings  

A. Weimholt derived this selfdual hexahedron as the vertex figure of bidex in 2004, and reused it as the cells of tridex in 2005.

There is a vertex 4-coloring of ike. Diminishing the vertices of a single color then derives teddi by chopping off 3 peppies. Diminishing the vertices of 2 such colors derives this selfdual hexahedron; peppies then already would intersect, this is where the f-edges originate from. Diminishing 3 colors will result in the dual of teddi, and at all 4 colors results in the dual of ike, i.e. in doe.

Its faces are 4 (x,f,f)-triangles (i.e. ox&#f) and 2 (x,x,x,f)-trapezia (or xf&#x). It is a self-dual chiral polyhedron, in fact the dual is nothing but a rotated copy, i.e. dualization here even respects the handedness!


Incidence matrix

2 * * | 1 1 1 1 0 0 | 2 1 1  verf = ovo&#(v,x)t
* 2 * | 0 1 1 0 1 0 | 1 1 1  verf = of&#x
* * 2 | 0 0 0 1 1 1 | 0 1 2  verf = of&#x
------+-------------+------
2 0 0 | 1 * * * * * | 2 0 0  f-edge
1 1 0 | * 2 * * * * | 1 1 0  f-edges
1 1 0 | * * 2 * * * | 1 0 1  x-edges
1 0 1 | * * * 2 * * | 0 1 1  f-edges
0 1 1 | * * * * 2 * | 0 1 1  x-edges
0 0 2 | * * * * * 1 | 0 0 2  x-edge
------+-------------+------
2 1 0 | 1 1 1 0 0 0 | 2 * *  ox&#f
1 1 1 | 0 1 0 1 1 0 | * 2 *  ox&#f
1 1 2 | 0 0 1 1 1 1 | * * 2  xf&#x

© 2004-2018
top of page