In geometry, a triakis tetrahedron (or kistetrahedron[1]) is a Catalan solid with 12 faces. Each Catalan solid is the dual of an Archimedean solid. The dual of the triakis tetrahedron is the truncated tetrahedron.
The triakis tetrahedron can be seen as a tetrahedron with a triangular pyramid added to each face; that is, it is the Kleetope of the tetrahedron. It is very similar to the net for the 5-cell, as the net for a tetrahedron is a triangle with other triangles added to each edge, the net for the 5-cell a tetrahedron with pyramids attached to each face. This interpretation is expressed in the name.
The length of the shorter edges is 3/5 that of the longer edges.[2] If the triakis tetrahedron has shorter edge length 1, it has area 5/3√11 and volume 25/36√2.
^Conway, Symmetries of things, p.284
^"Triakis Tetrahedron - Geometry Calculator".
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solid. The dual of the triakistetrahedron is the truncated tetrahedron. The triakistetrahedron can be seen as a tetrahedron with a triangular pyramid...
In geometry, the truncated triakistetrahedron, or more precisely an order-6 truncated triakistetrahedron, is a convex polyhedron with 16 faces: 4 sets...
tessellate three-dimensional space, making the triakis truncated tetrahedral honeycomb. The triakis truncated tetrahedron is the shape of the Voronoi cell of the...
hexagonal antiprism, D6d symmetry, order 24 Triakistetrahedron – 12 isosceles triangles, dual of truncated tetrahedron, Td symmetry, order 24 Other less regular...
A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection...
solid with genuine tetrahedral symmetry is the triakistetrahedron (dual of the truncated tetrahedron). The rhombic dodecahedron and tetrakis hexahedron...
vertices), or triakistetrahedron. Building a pyramid on each face of a regular octahedron, using twelve Sonobe units, results in a triakis octahedron....
octahedron. The symmetries of a regular tetrahedron correspond to those of a cube which map each tetrahedron to itself; the other symmetries of the cube...
Great rhombihexacron Great stellapentakis dodecahedron Great triakis icosahedron Great triakis octahedron Great triambic icosahedron Medial deltoidal hexecontahedron...
The truncated triakis icosahedron, or more precisely an order-10 truncated triakis icosahedron, is a convex polyhedron with 72 faces: 10 sets of 3 pentagons...
The truncated triakis octahedron, or more precisely an order-8 truncated triakis octahedron, is a convex polyhedron with 30 faces: 8 sets of 3 pentagons...
Victor Klee. The triakistetrahedron is the Kleetope of a tetrahedron, the triakis octahedron is the Kleetope of an octahedron, and the triakis icosahedron...
octahedron is the dual polyhedron of a cube. It is also a rectified tetrahedron, a square bipyramid in any of three orthogonal orientations, and a triangular...
4 stellations of the rhombic dodecahedron 187 stellations of the triakistetrahedron 358,833,097 stellations of the rhombic triacontahedron 17 stellations...
convex solids, this is the convex hull. The tetrahedron is self-dual, so the dual compound of a tetrahedron with its dual is the regular stellated octahedron...
(left) has 4 hexagons and tetrahedral symmetry as in a truncated triakistetrahedron. Hexagonal barrel (middle) has 8 hexagons and D6 symmetry. Soccer...
figure Symmetry group U# K# V E F Faces by type 6 Truncated tetrahedrontriakistetrahedron 2 3|3 3.6.6 Td U02 K07 12 18 8 4{3} + 4{6} 7 Truncated octahedron...
construction it has the same topology as the convex Catalan solid, the triakis octahedron, which has much shorter pyramids. It is a facetting of the cube...
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