Tetrakis cuboctahedron

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Tetrakis cuboctahedron
Rank3
Notation
Conway notationk4aC
Elements
Faces
Edges24+24
Vertices6+12
Vertex figure
Measures (edge length 1)
Central density1
Number of external pieces32
Level of complexity4
Related polytopes
ArmyTetrakis cuboctahedron
RegimentTetrakis cuboctahedron
DualChamfered cube
ConjugateNone
Abstract & topological properties
Flag count192
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryB3, order 48
Flag orbits4
ConvexYes
NatureTame


The tetrakis cuboctahedron is a convex polyhedron. It has 32 triangular faces: 24 isosceles triangles and 8 equilateral triangles.

It is topologically equivalent to an octahedron with each of its edges bisected and new edges created between the new vertices, thus dividing the faces into four smaller triangles.

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