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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: 10 sets of 3 pentagons arranged in an icosahedral symmetry, icosahedral arrangement, with 12 decagons in the gaps. Triakis icosahedron It is constructed from taking 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] |
Truncated Triakis Icosahedron
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 an icosahedral symmetry, icosahedral arrangement, with 12 decagons in the gaps. Triakis icosahedron It is constructed from taking 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 (or kisicosahedronConway, Symmetries of things, p.284) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated dodecahedron. Cartesian coordinates Let \phi be the golden ratio. The 12 points given by (0, \pm 1, \pm \phi) and cyclic permutations of these coordinates are the vertices of a regular icosahedron. Its dual regular dodecahedron, whose edges intersect those of the icosahedron at right angles, has as vertices the points (\pm 1, \pm 1, \pm 1) together with the points (\pm\phi, \pm 1/\phi, 0) and cyclic permutations of these coordinates. Multiplying all coordinates of this dodecahedron by a factor of (7\phi-1)/11\approx 0.938\,748\,901\,93 gives a slightly smaller dodecahedron. The 20 vertices of this dodecahedron, together with the vertices of the icosahedron, are the vertices of a triakis icosahedron centered at the origin. The length of its long edges equals 2. Its faces are isosceles triangles with one obtuse angl ... [...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 arrangement, with 8 regular hexagons in the gaps. Construction It is constructed from taking a tetrakis cube by 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 In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra ba ... [...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 taking 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. See also * Truncated triakis tetrahedron * Truncated tetrakis cube * Truncated triakis icosahedron External links George Hart's Polyhedron generator - "t8kO" (Conway polyhedron notation) Polyhedra Truncated tilings {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Triakis Tetrahedron
In geometry, 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. Construction It is constructed from a triakis tetrahedron by truncating the order-6 vertices. This creates 4 regular hexagon faces, and leaves 12 mirror-symmetric pentagons. A topologically similar equilateral polyhedron can be constructed by using 12 regular pentagons with 4 equilateral but nonplanar hexagons, each vertex with internal angles alternating between 108 and 132 degrees. Topologically, as a near-miss Johnson solid, the four hexagons corresponding to the face planes of a tetrahedron are triambi, with equal edges but alternating angles, while the pentagons only have reflection symmetry. Full truncation If all of a triakis tetrahedron's vertices, of both kinds, are truncated, the resulting solid is an irregular icosahedron, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway K10tD Net
Conway may refer to: Places United States * Conway, Arkansas * Conway County, Arkansas * Lake Conway, Arkansas * Conway, Florida * Conway, Iowa * Conway, Kansas * Conway, Louisiana * Conway, Massachusetts * Conway, Michigan * Conway Township, Michigan * Conway, Missouri * Conway, New Hampshire, a New England town ** Conway (CDP), New Hampshire, village in the town * Conway, North Dakota * Conway, North Carolina * Conway, Pennsylvania * Conway, South Carolina * Conway River (Virginia) * Conway, Washington Elsewhere * Conway, Queensland, a locality in the Whitsunday Region, Queensland, Australia * Conway River (New Zealand) * Conway, Wales, now spelt Conwy, a town with a castle in North Wales * River Conway, Wales, similarly respelt River Conwy Ships * HMS ''Conway'' (school ship) * HMS ''Conway'' (1832), a 26-gun sixth rate launched in 1832 * USS ''Conway'' (DD-70) or USS ''Craven'' (DD-70), a Caldwell class destroyer launched in 1918 * USS ''Conway'' (DD-507), a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway K10tD
Conway may refer to: Places United States * Conway, Arkansas * Conway County, Arkansas * Lake Conway, Arkansas * Conway, Florida * Conway, Iowa * Conway, Kansas * Conway, Louisiana * Conway, Massachusetts * Conway, Michigan * Conway Township, Michigan * Conway, Missouri * Conway, New Hampshire, a New England town ** Conway (CDP), New Hampshire, village in the town * Conway, North Dakota * Conway, North Carolina * Conway, Pennsylvania * Conway, South Carolina * Conway River (Virginia) * Conway, Washington Elsewhere * Conway, Queensland, a locality in the Whitsunday Region, Queensland, Australia * Conway River (New Zealand) * Conway, Wales, now spelt Conwy, a town with a castle in North Wales * River Conway, Wales, similarly respelt River Conwy Ships * HMS ''Conway'' (school ship) * HMS ''Conway'' (1832), a 26-gun sixth rate launched in 1832 * USS ''Conway'' (DD-70) or USS ''Craven'' (DD-70), a Caldwell class destroyer launched in 1918 * USS ''Conway'' (DD-507), a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Dodecahedron
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Geometric relations This polyhedron can be formed from a regular dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated icosahedral honeycomb. Area and volume The area ''A'' and the volume ''V'' of a truncated dodecahedron of edge length ''a'' are: :\begin A &= 5 \left(\sqrt+6\sqrt\right) a^2 &&\approx 100.990\,76a^2 \\ V &= \tfrac \left(99+47\sqrt\right) a^3 &&\approx 85.039\,6646a^3 \end Cartesian coordinates Cartesian coordinates for the vertices of a truncated dodecahedron with edge length 2''φ'' − 2, centered at the origin, are all even permutations of: :(0, ±, ±(2 + ''φ'')) :(±, ±''φ'', ±2''φ'') :(±''φ'', ±2, ±(''φ'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedron Truncated 12 Max
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Definition Convex polyhedra are well-defined, with several equivalent standard definitions. However, the formal mathematical definition of polyhedra that are not required to be convex has been problematic. Many definitions of "polyhedron" have been given within particular contexts,. some more rigorous than others, and there is not universal agreement over which of these to choose. Some of these definitions exclude shapes that have often been counted as polyhedra (such as the self-crossing polyhedra) or include shapes that are often not considered as valid polyhedra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decagonal Pyramid
In geometry, a pyramid () is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a ''lateral face''. It is a conic solid with polygonal base. A pyramid with an base has vertices, faces, and edges. All pyramids are self-dual. A right pyramid has its apex directly above the centroid of its base. Nonright pyramids are called oblique pyramids. A regular pyramid has a regular polygon base and is usually implied to be a ''right pyramid''. When unspecified, a pyramid is usually assumed to be a ''regular'' square pyramid, like the physical pyramid structures. A triangle-based pyramid is more often called a tetrahedron. Among oblique pyramids, like acute and obtuse triangles, a pyramid can be called ''acute'' if its apex is above the interior of the base and ''obtuse'' if its apex is above the exterior of the base. A right-angled pyramid has its apex above an edge or vertex of the base. In a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Dodecahedron
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Geometric relations This polyhedron can be formed from a regular dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated icosahedral honeycomb. Area and volume The area ''A'' and the volume ''V'' of a truncated dodecahedron of edge length ''a'' are: :\begin A &= 5 \left(\sqrt+6\sqrt\right) a^2 &&\approx 100.990\,76a^2 \\ V &= \tfrac \left(99+47\sqrt\right) a^3 &&\approx 85.039\,6646a^3 \end Cartesian coordinates Cartesian coordinates for the vertices of a truncated dodecahedron with edge length 2''φ'' − 2, centered at the origin, are all even permutations of: :(0, ±, ±(2 + ''φ'')) :(±, ±''φ'', ±2''φ'') :(±''φ'', ±2, ±(''φ'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
