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The triakis truncated tetrahedron is a polyhedron constructed from a truncated tetrahedron by adding three tetrahedrons onto its triangular faces, as interpreted by the name "triakis". It is classified as plesiohedron , meaning it can tessellate in three-dimensional space known as honeycomb ; an example is triakis truncated tetrahedral honeycomb .
In geometry, the rectified truncated tetrahedron is a polyhedron, constructed as a rectified, truncated tetrahedron. It has 20 faces: 4 equilateral triangles , 12 isosceles triangles , and 4 regular hexagons .
It can be used to tessellate three-dimensional space, making the triakis truncated tetrahedral honeycomb. [1] [2] The triakis truncated tetrahedron is the shape of the Voronoi cell of the carbon atoms in diamond, which lie on the diamond cubic crystal structure. [3] [4] As the Voronoi cell of a symmetric space pattern, it is a plesiohedron. [5]
In geometry, the truncated triakis tetrahedron is a convex polyhedron with 16 faces: four sets of three pentagons with a shared vertex, arranged in a tetrahedral arrangement, with four hexagons in the remaining gaps. The faces cannot all be regular polygons, so it is a near-miss Johnson solid.
The augmented truncated tetrahedron is constructed from a truncated tetrahedron by attaching a triangular cupola. [1] This cupola covers one of the truncated tetrahedron's four hexagonal faces, so that the resulting polyhedron's faces are eight equilateral triangles, three squares, and three regular hexagons. [2]
The tetrahedron is yet related to another two solids: By truncation the tetrahedron becomes a truncated tetrahedron. The dual of this solid is the triakis tetrahedron , a regular tetrahedron with four triangular pyramids attached to each of its faces. i.e., its kleetope .
This uniform polyhedron compound is a composition of two truncated tetrahedra, formed by truncating each of the tetrahedra in the stellated octahedron.It is related to the cantic cube construction of the truncated tetrahedron, as , which is one of the two dual positions represented in this compound.
They are the cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron, icosidodecahedron, truncated cuboctahedron, truncated icosahedron, truncated dodecahedron, and the truncated tetrahedron. [10] The dual polyhedron of an Archimedean solid is a Catalan solid. [1]