Triakis tetrahedron
Template:Short description Template:Infobox polyhedron File:Triakis tetrahedron.stl In geometry, a triakis tetrahedron (or tristetrahedronTemplate:R, or kistetrahedronTemplate:R) is a solid constructed by attaching four triangular pyramids onto the triangular faces of a regular tetrahedron, a Kleetope of a tetrahedron.Template:R This replaces the triangular faces with three, so there are twelve in total; eight vertices and eighteen edges form them.Template:R This interpretation is also expressed in the name, triakis, which is used for the Kleetopes of polyhedra with triangular faces.Template:R
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 .Template:R Unlike its dual, the truncated tetrahedron has no vertex-transitive, but rather face-transitive, meaning its solid appearance is unchanged by any transformation like reflecting and rotation between two triangular faces.Template:R Whenever a triakis tetrahedron has a hole, it is possible for a polyhedron to exist with the same or larger size passing through it.Template:R