Compound of six tetrahedra

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Compound of six tetrahedra
Rank3
TypeUniform
Notation
Bowers style acronymSnu
Elements
Components6 tetrahedra
Faces24 triangles
Edges12+24
Vertices24
Vertex figureEquilateral triangle, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Volume
Dihedral angle
Central density6
Number of external pieces120
Level of complexity20
Related polytopes
ArmySemi-uniform Toe, edge lengths (squares), (between ditrigons)
RegimentSnu
DualCompound of six tetrahedra
ConjugateCompound of six tetrahedra
Convex coreTetrakis hexahedron
Abstract & topological properties
Flag count144
Schläfli type{3,3}
OrientableYes
Properties
SymmetryB3, order 48
Flag orbits3
ConvexNo
NatureTame

The snubahedron, snu, or compound of six tetrahedra is a uniform polyhedron compound. It consists of 24 triangles, with three faces joining at a vertex.

This is a special case of the more general small snubahedron, with double symmetry. It can be formed from the rhombihexahedron by replacing each of the cubes with the inscribed stella octangula.

Its quotient prismatic equivalent is the tetrahedral hexateroorthowedge, which is eight-dimensional.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a small snubahedron of edge length 1 are given by all permutations of:

  • .

External links[edit | edit source]