Diminished rectified order-6 truncated triakis tetrahedron

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Diminished rectified order-6 truncated triakis tetrahedron
Rank3
TypeNear-miss
Elements
Faces3+3+3+3 isosceles triangles, 6 irregular pentagons, 1 hexagon, 1 dodecagon
Edges6+6+6+6+6+3+3+3+3
Vertices6+6+6+3+3
Vertex figures6+6 scalene triangles
 6 irregular quadrilateral
 3+3 isosceles trapezoid
Measures (edge length 1)
Edge length ratio1.04774
Central density1
Number of external pieces20
Related polytopes
ConjugateNone
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×I
ConvexYes
NatureTame

The diminished rectified order-6 truncated triakis tetrahedron is a near-miss Johnson solid. Its faces are 3+3+3+3 isosceles triangles, 6 irregular pentagons, 1 hexagon and 1 dodecagon.

It can be called a hexagonal rotunda, due to its visual similarity to the pentagonal rotunda. That being said, there's not actually a family of rotunda-like shapes that contains both of these.

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