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  
External
links
polytopewiki  

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

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