Triangular antitegum

From Polytope Wiki
(Redirected from Trigonal trapezohedra)
Jump to navigation Jump to search
Triangular antitegum
Rank3
TypeIsotopic
Notation
Bowers style acronymTrate
Coxeter diagramp2p6o ()
Elements
Faces6 rhombi
Edges6+6
Vertices2+6
Vertex figure6 isosceles triangles, 2 triangles
Measures (edge length 1)
Central density1
Related polytopes
ArmyTrate
RegimentTrate
DualTriangular antiprism
ConjugateTriangular antitegum
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(G2×A1)/2, order 12
ConvexYes
NatureTame

The triangular antitegum, also known as the trigonal trapezohedron, is an antitegum based on a triangle. If all angles are equal, the result is the regular cube. The general triangular antitegum has 6 identical rhombic faces.

Variants of the triangular antitegum exist that are dual to the triangular antipodium as well, using 2 different sets of 3 kites for faces.