| Truncated triakis octahedron | |
|---|---|
 | |
| Conway notation | t8kO = dk8tC |
| Faces | 6 octagons 24 pentagons |
| Edges | 84 |
| Vertices | 56 |
| Dual | Octakis truncated cube |
| Vertex configuration | 8 (5.5.5) 48 (5.5.8) |
| Symmetry group | Oh |
| Properties | convex |
 Net | |
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 arranged in an octahedral arrangement, with 6 octagons in the gaps.
It is constructed from taking a triakis octahedron by truncating the order-8 vertices. This creates 6 regular octagon faces, and leaves 24 mirror-symmetric pentagons.
 Triakis octahedron |
The dual of the order-8 truncated triakis octahedron is called a octakis truncated cube. It can be seen as a truncated cube with octagonal pyramids augmented to the faces.
 Truncated cube |  Octakis truncated cube |  Net |
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In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.
In geometry, an octahedron is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
In geometry, the truncated octahedron is an Archimedean solid. It has 14 faces, 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a zonohedron. It is also the Goldberg polyhedron GIV(1,1), containing square and hexagonal faces. Like the cube, it can tessellate 3-dimensional space, as a permutohedron.
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces, 36 edges, and 24 vertices.
In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges. Since each of its faces has point symmetry, the truncated cuboctahedron is a zonohedron. The truncated cuboctahedron can tessellate with the octagonal prism.
In geometry, a triakis octahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube.
In geometry, a truncated 24-cell is a uniform 4-polytope formed as the truncation of the regular 24-cell.
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates from Kepler's names for the Archimedean solids.
In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations.
The truncated triakis tetrahedron, or more precisely an order-6 truncated triakis tetrahedron, is a convex polyhedron with 16 faces: 4 sets of 3 pentagons arranged in a tetrahedral arrangement, with 4 hexagons in the gaps.
A tetradecahedron is a polyhedron with 14 faces. There are numerous topologically distinct forms of a tetradecahedron, with many constructible entirely with regular polygon faces.
In geometry and polyhedral combinatorics, the Kleetope of a polyhedron or higher-dimensional convex polytope P is another polyhedron or polytope PK formed by replacing each facet of P with a shallow pyramid. Kleetopes are named after Victor Klee.
The truncated rhombicuboctahedron is a polyhedron, constructed as a truncated rhombicuboctahedron. It has 50 faces, 18 octagons, 8 hexagons, and 24 squares. It can fill space with the truncated cube, truncated tetrahedron and triangular prism as a truncated runcic cubic honeycomb.
In geometry, chamfering or edge-truncation is a topological operator that modifies one polyhedron into another. It is similar to expansion, moving faces apart and outward, but also maintains the original vertices. For polyhedra, this operation adds a new hexagonal face in place of each original edge.
In geometry, an icosahedron is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi), meaning 'twenty', and ἕδρα (hédra), meaning 'seat'. The plural can be either "icosahedra" or "icosahedrons".
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 arranged in a icosahedral arrangement, with 12 decagons in the gaps.
The truncated tetrakis cube, or more precisely an order-6 truncated tetrakis cube, is a convex polyhedron with 32 faces: 24 sets of 3 pentagons arranged in an octahedral arrangement, with 8 hexagons in the gaps.