Augmented truncated tetrahedron

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Augmented truncated tetrahedron
Augmented truncated tetrahedron 2.png
Rank3
TypeCRF
SpaceSpherical
Notation
Bowers style acronymAutut
Coxeter diagramxxoo3oxux&#xt
Elements
Faces1+1+3+3 triangles, 3 squares, 3 hexagons
Edges3+3+3+3+3+6+6
Vertices3+3+3+6
Vertex figures3 rectangle, edge length 1 and 2
 6 irregular tetragons, edge length 1, 2, 1, 3
 3+3 isosceles triangles, edge lengths 1, 3, 3
Measures (edge length 1)
Volume
Dihedral angles3–4 join:
 3–6 join:
 3–4 cupolaic:
 3–6 tut:
 6–6:
Central density1
Related polytopes
ArmyAutut
RegimentAutut
DualRhombirhombistellated triakis tetrahedron
ConjugateAugmented truncated tetrahedron
Abstract properties
Euler characteristic2
Topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×I, order 6
ConvexYes
NatureTame

The augmented truncated tetrahedron, or autut, is one of the 92 Johnson solids (J65). It consists of 1+1+3+3 triangles, 3 squares, and 3 hexagons. It can be constructed by attaching a triangular cupola to one of the hexagonal faces of the truncated tetrahedron..

Vertex coordinates[edit | edit source]

An augmented truncated tetrahedron of edge length 1 has vertices given by all even sign changes of:

Plus all permutations of:

External links[edit | edit source]