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Given the edge length .The surface area of a truncated tetrahedron is the sum of 4 regular hexagons and 4 equilateral triangles' area, and its volume is: [2] =, =.. The dihedral angle of a truncated tetrahedron between triangle-to-hexagon is approximately 109.47°, and that between adjacent hexagonal faces is approximately 70.53°.
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]
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]
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] Since it has the property of convexity and has regular polygonal faces, the augmented truncated tetrahedron is a Johnson solid , denoted as the sixty ...
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.
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 truncated tetrahedron-first Schlegel diagram projection of the truncated 5-cell into 3-dimensional space has the following structure: The projection envelope is a truncated tetrahedron . One of the truncated tetrahedral cells project onto the entire envelope.