Triakis triangular tegum

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Triakis triangular tegum
Rank3
Elements
Faces6 isosceles triangles, 12 scalene triangles
Edges3+6+6+12
Vertices2+3+6
Vertex figures2 triambi
 3 rectangular-symmetric octagons
 6 isosceles triangles
Measures (edge length 1)
Central density1
Related polytopes
DualTruncated triangular prism
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×A1, order 12
ConvexYes
NatureTame

The triakis triangular tegum is a polyhedron formed from the triangular tegum by augmenting its faces with shallow triangular pyramids. It has 6 isosceles triangles and 12 scalene triangles as faces.

The canonical variant with midradius 1 has four edge lengths: one of length , one of length , one of length and the other of length .

Vertex coordinates[edit | edit source]

The vertices of a canonical triakis triangular tegum of midradius 1 are given by:

In vertex figures[edit | edit source]

A variant of the triakis triangular tegum with (A2×A1)+ symmetry occurs as the vertex figure of the tetrafold tetraswirlchoron.

Vertex figure of the tetrafold tetraswirlchoron.