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Triakis octahedron
Catalan solid with 24 faces / From Wikipedia, the free encyclopedia
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In geometry, a triakis octahedron (or trigonal trisoctahedron[1] or kisoctahedron[2]) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube.
Triakis octahedron | |
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![]() (Click here for rotating model) | |
Type | Catalan solid |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() |
Conway notation | kO |
Face type | V3.8.8![]() isosceles triangle |
Faces | 24 |
Edges | 36 |
Vertices | 14 |
Vertices by type | 8{3}+6{8} |
Symmetry group | Oh, B3, [4,3], (*432) |
Rotation group | O, [4,3]+, (432) |
Dihedral angle | 147°21′00″ arccos(−3 + 8√2/17) |
Properties | convex, face-transitive |
![]() Truncated cube (dual polyhedron) |
![]() Net |
It can be seen as an octahedron with triangular pyramids added to each face; that is, it is the Kleetope of the octahedron. It is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron. Both names reflect that it has three triangular faces for every face of an octahedron. The tetragonal trisoctahedron is another name for the deltoidal icositetrahedron, a different polyhedron with three quadrilateral faces for every face of an octahedron.
This convex polyhedron is topologically similar to the concave stellated octahedron. They have the same face connectivity, but the vertices are at different relative distances from the center.
If its shorter edges have length of 1, its surface area and volume are: