Triakis tetrahedron
Catalan solid with 12 faces From Wikipedia, the free encyclopedia
In geometry, a triakis tetrahedron (or tristetrahedron[1], or kistetrahedron[2]) is a solid constructed by attaching four triangular pyramids onto the triangular faces of a regular tetrahedron, a Kleetope of a tetrahedron.[3] This replaces the triangular faces with three, so there are twelve in total; eight vertices and eighteen edges form them.[4] This interpretation is also expressed in the name, triakis, which is used for the Kleetopes of polyhedra with triangular faces.[2]
Triakis tetrahedron | |
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Type | Catalan solid, Kleetope |
Faces | 12 |
Edges | 18 |
Vertices | 8 |
Symmetry group | tetrahedral symmetry |
Dihedral angle (degrees) | 129.52° |
Dual polyhedron | truncated tetrahedron |
Properties | convex, face-transitive, Rupert property |
Net | |
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The triakis tetrahedron is a Catalan solid, the dual polyhedron of a truncated tetrahedron, an Archimedean solid with four hexagonal and four triangular faces, constructed by cutting off the vertices of a regular tetrahedron; it shares the same symmetry of full tetrahedral . Each dihedral angle between triangular faces is .[4] Unlike its dual, the truncated tetrahedron is not vertex-transitive, but rather face-transitive, meaning its solid appearance is unchanged by any transformation like reflecting and rotation between two triangular faces.[5] Whenever a triakis tetrahedron has a hole, it is possible for a polyhedron to exist with the same or larger size passing through it.[6]
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