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Truncated Triakis Icosahedron
The truncated triakis icosahedron, or more precisely an order-10 truncated triakis icosahedron, is a convex polyhedron with 72 faces: 20 sets of 3 pentagons arranged in an icosahedral symmetry, icosahedral arrangement, with 12 decagons in the gaps. Triakis icosahedron It is constructed from a triakis icosahedron by Truncation (geometry), truncating the order-10 vertices. This creates 12 regular decagon faces, and leaves 60 mirror-symmetric pentagons. Decakis truncated dodecahedron The dual of the ''truncated triakis icosahedron'' is called a decakis truncated dodecahedron. It can be seen as a truncated dodecahedron with decagonal pyramids augmented to the faces. See also * Truncated triakis tetrahedron * Truncated triakis octahedron * Truncated tetrakis cube External links George Hart's Polyhedron generator - "t10kI" (Conway polyhedron notation) Polyhedra Truncated tilings {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triakis Icosahedron
In geometry, the triakis icosahedron is an Archimedean dual solid, or a Catalan solid, with 60 isosceles triangle faces. Its dual is the truncated dodecahedron. It has also been called the kisicosahedron. It was first depicted, in a non-convex form with equilateral triangle faces, by Leonardo da Vinci in Luca Pacioli's ''Divina proportione'', where it was named the ''icosahedron elevatum''. The capsid of the Hepatitis A virus has the shape of a triakis icosahedron. As a Kleetope The triakis icosahedron can be formed by gluing triangular pyramids to each face of a regular icosahedron. Depending on the height of these pyramids relative to their base, the result can be either convex or non-convex. This construction, of gluing pyramids to each face, is an instance of a general construction called the Kleetope; the triakis icosahedron is the Kleetope of the icosahedron. This interpretation is also expressed in the name, triakis, which is used for the Kleetopes of polyhedra with tria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Tetrakis Cube
The truncated tetrakis cube, or more precisely an order-6 truncated tetrakis cube or hexatruncated tetrakis cube, is a convex polyhedron with 32 faces: 24 sets of 3 bilateral symmetry pentagons arranged in an Octahedral symmetry, octahedral arrangement, with 8 regular hexagons in the gaps. Construction It is constructed from a tetrakis cube by Truncation (geometry), truncating the order-6 vertices. This creates 4 regular hexagon faces, and leaves 12 mirror-symmetric pentagons. Hexakis truncated octahedron The dual of the ''order-6 truncated triakis tetrahedron'' is called a hexakis truncated octahedron. It is constructed by a truncated octahedron with hexagonal pyramids augmented. See also * Truncated triakis tetrahedron * Truncated triakis octahedron * Truncated triakis icosahedron External links George Hart's Polyhedron generator - "t6kC" (Conway polyhedron notation) Polyhedra {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Triakis Octahedron
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 symmetry, octahedral arrangement, with 6 octagons in the gaps. Triakis octahedron It is constructed from a triakis octahedron by Truncation (geometry), truncating the order-8 vertices. This creates 6 regular octagon faces, and leaves 24 mirror-symmetric pentagons. Octakis truncated cube 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. Uses The DaYan Gem 6 is a Combination puzzle, twisty puzzle in this shape. See also * Truncated triakis tetrahedron * Truncated tetrakis cube * Truncated triakis icosahedron References External links George Hart's Polyhedron generator - "t8kO" (Conway polyhedron notation) Polyhedra Truncated tilings {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
