Triakis tetrahedron
In geometry, a triakis tetrahedron is a Catalan solid, constructed by attaching four triangular pyramids to a tetrahedron.
As a Kleetope
The triakis tetrahedron is constructed by attaching four triangular pyramids onto the triangular faces of a regular tetrahedron, a Kleetope of a tetrahedron. This replaces the equilateral triangular faces of the regular tetrahedron with three isosceles triangles at each face, so there are twelve in total; eight vertices and eighteen edges form them. This interpretation is also expressed in the name, triakis, which is used for Kleetopes of polyhedra with triangular faces.As a Catalan solid
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. 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. The triakis tetrahedron can pass through a copy of itself of the same size, but it is an exceptionally tight squeeze: the largest known triakis tetrahedron that can pass through is only about 1.000004 times larger.The triakis tetrahedron is the stacked polyhedron that is a non-ideal. Combinatorially, it has independent set of exactly half the vertices but is not bipartite, so neither can be realized as an ideal polyhedron.