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Archimedean solid with 14 faces
In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six equilateral square pyramids, one
Truncated_octahedron
Archimedean solid with 26 faces
media related to Truncated cuboctahedron. Cube Cuboctahedron Octahedron Truncated icosidodecahedron Truncated octahedron – truncated tetratetrahedron
Truncated_cuboctahedron
Archimedean solid with 14 faces
truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and δS +1, where δS is the silver ratio, √2 +1. The truncated
Truncated_cube
Convex polyhedron with 38 faces
In geometry, the rectified truncated octahedron is a convex polyhedron, constructed as a rectified, truncated octahedron. It has 38 faces: 24 isosceles
Rectified truncated octahedron
Rectified_truncated_octahedron
Geometric operation which truncates the edges of polyhedra
.. The truncated octahedron or truncated icosahedron, GP(1,1), creates a Goldberg sequence: GP(1,1), GP(2,2), GP(4,4), GP(8,8)... A truncated tetrakis
Chamfer_(geometry)
pentagons. 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
Truncated_triakis_octahedron
Polyhedron with eight triangular faces
geometry, an octahedron (pl.: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid
Octahedron
Isogonal polyhedron with regular faces
the five truncations of the Platonic solids—truncated tetrahedron, truncated octahedron, truncated cube, truncated dodecahedron, and truncated icosahedron—and
Uniform_polyhedron
Catalan solid with 24 faces
tetrakis cube, and kiscube) is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid. It can be called a disdyakis hexahedron or
Tetrakis_hexahedron
Type of tesseract
remaining 6 truncated octahedral cells. The remaining gap between the inscribed truncated octahedron and the envelope are filled by 8 flattened truncated tetrahedra
Truncated_tesseract
Polyhedron with 20 faces
called a snub octahedron, snub tetratetrahedron, snub tetrahedron, and pseudo-icosahedron. This can be seen as an alternated truncated octahedron. If all the
Icosahedron
Shape with six sides
the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron
Hexagon
Near-miss Johnson solid with 92 faces
Near-miss Johnson solid Rectified truncated tetrahedron Rectified truncated octahedron Rectified truncated cube Rectified truncated dodecahedron "PolyHédronisme"
Rectified truncated icosahedron
Rectified_truncated_icosahedron
Convex polyhedron projected from hypercube
and a truncated octahedron forms the truncated cuboctahedron, while the Minkowski sum of the cube and the rhombic dodecahedron forms the truncated rhombic
Zonohedron
Solid with eight equal triangular faces
regular octahedron is an eight-sided polyhedron with equilateral triangles as its faces. Known for its highly symmetrical form, the regular octahedron is a
Regular_octahedron
regular 24-cell. There are two degrees of truncations, including a bitruncation. The truncated 24-cell or truncated icositetrachoron is a uniform 4-dimensional
Truncated_24-cells
Geometric object
hexakis truncated octahedron. It is constructed by a truncated octahedron with hexagonal pyramids augmented. Truncated triakis tetrahedron Truncated triakis
Truncated_tetrakis_cube
Primitive cell of crystal lattices with Voronoi decomposition applied
approximated the shape of the Wigner–Seitz cell in sodium, which is a truncated octahedron, as a sphere of equal volume, and solved the Schrödinger equation
Wigner–Seitz_cell
Catalan solid with 24 faces
triakis octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube. It
Triakis_octahedron
Polyhedron that tiles space by translation
hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron. Each parallelohedron is centrally symmetric with symmetric faces
Parallelohedron
Catalan solid with 30 faces
faces of different pyramids are coplanar. It can also be made from a truncated octahedron by dividing the hexagonal faces into three rhombi: Let φ be the golden
Rhombic_triacontahedron
Type of space-filling polyhedron
plesiohedra include the cube, hexagonal prism, rhombic dodecahedron, and truncated octahedron. The largest number of faces that a plesiohedron can have is 38.
Plesiohedron
Polyhedral compound
compound is a composition of two truncated tetrahedra, formed by truncating each of the tetrahedra in the stellated octahedron. It is related to the cantic
Compound of two truncated tetrahedra
Compound_of_two_truncated_tetrahedra
Method of describing higher-order polyhedra
Archimedean Truncated tetrahedron tT Cuboctahedron aC = aO = eT Truncated cube tC Truncated octahedron tO = bT Rhombicuboctahedron eC = eO truncated cuboctahedron
Conway_polyhedron_notation
Polyhedra in which all vertices are the same
cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron, icosidodecahedron, truncated cuboctahedron, truncated icosahedron, truncated dodecahedron
Archimedean_solid
Polytope whose vertices represent permutations
image on the right shows the permutohedron of order 4, which is the truncated octahedron. Its vertices are the 24 permutations of (1, 2, 3, 4). Parallel edges
Permutohedron
Operation that cuts polytope vertices, creating a new facet in place of each vertex
but leaving an interior part of the original faces. Example: a truncated octahedron is a bitruncated cube: t{3,4} = 2t{4,3}. A complete bitruncation
Truncation_(geometry)
Cahill–Keyes Polyhedral Compromise Gene Keyes Projects the globe onto a truncated octahedron with symmetrical components and contiguous land masses that may be
List_of_map_projections
Polyhedron with 8 rhombic and 4 hexagonal faces
elongated dodecahedron can be constructed as a contraction of a uniform truncated octahedron, where square faces are reduced to single edges and regular hexagonal
Elongated_dodecahedron
Mathematical foam of equal-volume bubbles
bitruncated cubic honeycomb, a convex uniform honeycomb formed by the truncated octahedron, a space-filling convex polyhedron with 6 square faces and 8 hexagonal
Weaire–Phelan_structure
Hemicube Hemi-octahedron Hemi-dodecahedron Hemi-icosahedron Archimedean solid Truncated tetrahedron Cuboctahedron Truncated cube Truncated octahedron Rhombicuboctahedron
List_of_mathematical_shapes
Operation in Euclidean geometry
3-polytopes), a bitruncated form is the truncated dual. For example, a bitruncated cube is a truncated octahedron. For a regular 4-polytope, a bitruncated
Bitruncation
Solid with six equal square faces
tetrakis hexahedron, dual to the truncated octahedron. The barycentric subdivision of a cube (or its dual, the regular octahedron) is the disdyakis dodecahedron
Cube
Self-intersecting uniform polyhedron
tetrahedron Octahedron 4.3⁄2.4.3 3⁄2 3 | 2 Truncated tetrahedron Cantellated tetrahedron (Cuboctahedron) Omnitruncated tetrahedron (Truncated octahedron)
Uniform_star_polyhedron
Mechanical puzzles
The Face Turning Octahedron (or Face-Turning Octahedron, often abbreviated as FTO) is a combination and mechanical puzzle. Unlike cubic puzzles, the FTO
Face_Turning_Octahedron
Regular tiling of hyperbolic 3-space
has octahedron and truncated dodecahedron cells, with a square pyramid vertex figure. It can be seen as analogous to the 2D hyperbolic truncated order-4
Order-4 dodecahedral honeycomb
Order-4_dodecahedral_honeycomb
Any of the five regular polyhedra
stellated octahedron. The coordinates of the icosahedron are related to two alternated sets of coordinates of a nonuniform truncated octahedron, t{3,4}
Platonic_solid
Geometric figure
Cyclotruncated pentachoric tetracomb Small truncated-pentachoric tetracomb The truncated 4-simplex honeycomb or truncated 5-cell honeycomb is a space-filling
5-cell_honeycomb
Partition of a toroidal surface into polygons
hull truncated cube truncated octahedron truncated octahedron expanded cuboctahedron truncated cuboctahedron truncated cuboctahedron truncated cuboctahedron
Toroidal_polyhedron
Natural number
numerals, 0–9, and the letters, A-Z. See Base 36. The truncated cube and the truncated octahedron are Archimedean solids with 36 edges. The number of domino
36_(number)
Polyhedron with 14 faces
stellated truncated hexahedron is a stellation of the truncated hexahedron, its core is a regular octahedron. It shares the vertex arrangement with three other
Stellated truncated hexahedron
Stellated_truncated_hexahedron
m = 30 {\displaystyle m=30} Truncated tetrahedron Truncated cube Truncated octahedron Truncated dodecahedron Truncated icosahedron A snark is a bridgeless
List_of_graphs
Flat-sided three-dimensional shape
through Pappus. Both cubical dice and 14-sided dice in the shape of a truncated octahedron in China have been dated back as early as the Warring States period
Polyhedron
Removal of alternate vertices
an alternation of a truncated regular or truncated quasiregular polyhedron. In general a polyhedron can be snubbed if its truncation has only even-sided
Alternation_(geometry)
dodecahedron Archimedean solid Truncated tetrahedron, Cuboctahedron, Truncated cube, Truncated octahedron, Rhombicuboctahedron, Truncated cuboctahedron, Snub cube
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Convex polyhedron made from hexagons and pentagons
faces. Simple examples of Goldberg polyhedra include the dodecahedron and truncated icosahedron. Other forms can be described by taking a chess knight move
Goldberg_polyhedron
Natural number
distinct fully supported stellations are also produced by truncated cube and truncated octahedron. Seventeen is also the number of four-dimensional parallelotopes
17_(number)
Isogonal polytope with uniform facets
the Schläfli symbol of the regular seed polytope. For example, the truncated octahedron is represented by the notation: t0,1{3,4}. In four dimensions, there
Uniform_polytope
Polyhedral compound
unique planes. It shares the same vertex arrangement as a nonuniform truncated octahedron, having irregular hexagons alternating with long and short edges
Compound_of_two_icosahedra
Marked objects for finding random numbers
Decahedron A ten-sided die made by truncating two opposite vertices of an octahedron. 11 Truncated sphere A truncated sphere with eleven landing positions
Dice
Topics referred to by the same term
Mecon may refer to: Truncated octahedron or mecon, an Archimedean solid Master of Economics (M.Econ.), a postgraduate master's degree MECON (company),
Mecon
Kepler–Poinsot polyhedron with 20 faces
tetrahedron symmetry of the icosahedron, as a partial faceting of the truncated octahedron (or omnitruncated tetrahedron): . It can also be constructed with
Great_icosahedron
E F Faces by type 6 Truncated tetrahedron triakis tetrahedron 2 3|3 3.6.6 Td U02 K07 12 18 8 4{3} + 4{6} 7 Truncated octahedron tetrakis hexahedron 2
List of Wenninger polyhedron models
List_of_Wenninger_polyhedron_models
Polyhedral compromise map projection
arrangement is an unfolding of a polyhedral globe with the shape of a truncated octahedron, evoking the butterfly map principle first developed by Bernard J
Waterman_butterfly_projection
Convex polyhedron whose faces are almost regular polygons
antiprism, Gyroelongated hexagonal pyramid Triangular cupola Truncated tetrahedron Truncated octahedron 4.4.4.4 Square icositetrahedron (Cube) 3.4.6.4: Hexagonal
Near-miss_Johnson_solid
hypercubic honeycomb Quarter hypercubic honeycomb Simplectic honeycomb Truncated simplicial honeycomb George Olshevsky, Uniform Panoploid Tetracombs, Manuscript
Omnitruncated simplicial honeycomb
Omnitruncated_simplicial_honeycomb
Semiregular tiling of a plane
shapes like the triakis icosahedron and triakis octahedron. It is the dual tessellation of the truncated hexagonal tiling which has one triangle and two
Truncated_hexagonal_tiling
Polyhedron with 14 faces
solids: Cuboctahedron (8 triangles, 6 squares) Truncated cube (8 triangles, 6 octagons) Truncated octahedron (6 squares, 8 hexagons) Prisms and antiprisms:
Tetradecahedron
Geometric operation applied to a polyhedron
alternated truncations, like the snub octahedron, as s { 3 , 4 } {\displaystyle s{\begin{Bmatrix}3,4\end{Bmatrix}}} , , is the alternation of the truncated octahedron
Snub_(geometry)
Convex polytope whose vertices all have integer Cartesian coordinates
Cube Cuboctahedron Octahedron Truncated octahedron (±1, ±1, ±1) (0, ±1, ±1) (0, 0, ±1) (0, ±1, ±2) Four integral polytopes in three dimensions
Integral_polytope
Tiling of euclidean or hyperbolic space of three or more dimensions
honeycomb Elongated dodecahedral honeycomb Bitruncated cubic honeycomb or truncated octahedra Other known examples of space-filling polyhedra include: The
Honeycomb_(geometry)
Natural number, composite number
vertices and is the only Catalan solid that can tessellate space. The truncated octahedron contains 14 faces, is the permutohedron of order four, and the only
14_(number)
Polyhedron formed by joining two prisms
regular faces capable of space-filling (the others being the cube, truncated octahedron, triangular prism, and hexagonal prism) and it is the only Johnson
Gyrobifastigium
Geodesic polyhedron with 180 faces
The hexapentakis truncated icosahedron is a convex polyhedron constructed as an augmented truncated icosahedron. It is a geodesic polyhedron {3,5+}3,0
Hexapentakis truncated icosahedron
Hexapentakis_truncated_icosahedron
Near-miss Johnson solid with 16 faces
faces of a truncated tetrahedron with pyramids. Truncated tetrakis cube Truncated triakis octahedron Truncated triakis icosahedron Chamfered dodecahedron Sloane
Truncated_triakis_tetrahedron
Archimedean solid with 8 faces
tetrahedron Triakis truncated tetrahedron Octahedron – a rectified tetrahedron Kuchel, Philip W. (2012). "96.45 Can you 'bend' a truncated truncated tetrahedron
Truncated_tetrahedron
Regular paracompact honeycomb
tetrahedral honeycomb, t0,1,2,3{6,3,3}, has truncated octahedron, hexagonal prism, dodecagonal prism, and truncated trihexagonal tiling cells, with an irregular
Hexagonal_tiling_honeycomb
honeycomb, ↔ , is composed of triangular tiling and octahedron cells, in a truncated octahedron vertex figure. The cantic order-4 hexagonal tiling honeycomb
Order-4 hexagonal tiling honeycomb
Order-4_hexagonal_tiling_honeycomb
Polyhedron which tiles 3D space
3-space, as do the five parallelohedra (the cube, hexagonal prism, truncated octahedron, elongated dodecahedron, and rhombic dodecahedron). Other space-filling
Space-filling_polyhedron
Edge-joined polygons which fold into a polyhedron
OEIS) Regular tetrahedron Prism Truncated Icosahedron Truncated dodecahedron Truncated cube Truncated octahedron Truncated cuboctahedron Rhombicuboctahedron
Net_(polyhedron)
Catalan solid with 48 faces
In geometry, a disdyakis dodecahedron, (also hexoctahedron, hexakis octahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron) or d48, is a
Disdyakis_dodecahedron
Polyhedron resulting from the snub operation
snubification of the truncated octahedron, truncated cuboctahedron and the truncated icosidodecahedron - the three convex truncated quasiregular polyhedra
Snub_polyhedron
Value determined from a polyhedron
combinations of the invariants for the Platonic solids. In particular, the truncated octahedron also tiles space and has Dehn invariant zero like the cube. The Dehn
Dehn_invariant
the truncated cube cells project to a truncated cube in the center of the projection envelope. Six octagonal prisms connect this central truncated cube
Runcinated_tesseracts
3D symmetry group
A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine
Octahedral_symmetry
Archimedean solid with 26 faces
obtain non-uniform hexagon faces Truncated rhombicuboctahedron, a rhombicuboctahedron with all of its vertices being truncated. Small cubicuboctahedron and
Rhombicuboctahedron
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
Truncated_triakis_icosahedron
polyhedra. The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively
List_of_uniform_polyhedra
augmented by attaching pyramids to faces, as showcased with the stellated octahedron. 1568: Wenzel Jamnitzer publishes Perspectiva Corporum Regularium, with
List of polyhedral stellations
List_of_polyhedral_stellations
American–Canadian animated television series
an open-world video game developed by Cora's mother, they touch a truncated octahedron-shaped game projector and say "Launch Skillsville" to prompt it to
Skillsville
Polyhedron with 24 faces
have chiral icosahedral symmetry: Four Catalan solids, convex: Triakis octahedron - isosceles triangles Tetrakis hexahedron - isosceles triangles Deltoidal
Icositetrahedron
Covering by shapes without overlaps or gaps
only Platonic polyhedron to do so), the rhombic dodecahedron, the truncated octahedron, and triangular, quadrilateral, and hexagonal prisms, among others
Tessellation
Convex polyhedron with 38 faces
polyhedra: Rectified truncated tetrahedron Rectified truncated octahedron Rectified truncated dodecahedron Rectified truncated icosahedron Coxeter Regular
Rectified_truncated_cube
In geometry, the 25 great circles of the spherical octahedron is an arrangement of 25 great circles in octahedral symmetry. It was first identified by
25 great circles of the spherical octahedron
25_great_circles_of_the_spherical_octahedron
Convex polyhedron that fills space isohedrally
Parallelohedra cube hexagonal prism rhombic dodecahedron elongated dodecahedron truncated octahedron
Stereohedron
Geometric operation
progressively-higher-dimensional polytopes: Uniform polytope truncation operators For regular polygons: An ordinary truncation, t 0 , 1 { p } = t { p } = { 2 p } {\displaystyle
Omnitruncation
Cupola with hexagonal base
of ratio 1 : 1 2 2 {\textstyle 1:{\frac {1}{2}}{\sqrt {2}}} . The truncated octahedron can be constructed by attaching eight of those same triangular cupolas
Triangular_cupola
Notation for a polyhedron's vertex figure
solids: Truncated tetrahedron: 3.6.6 (12) Truncated cube: 3.8.8 (24) Truncated dodecahedron: 3.10.10 (60) Truncated octahedron: 4.6.6 (24) Truncated cuboctahedron:
Vertex_configuration
Number of available physical states per energy unit
First Brillouin zone of the FCC lattice, a truncated octahedron, showing symmetry labels for high symmetry lines and points
Density_of_states
Polyhedral compound
Francesca includes a drawing of an octahedron circumscribed around a cube, with eight of the cube edges lying in the octahedron's eight faces. Three cubes inscribed
Compound_of_three_cubes
Quasiregular space-filling tesselation
an order-3 truncated triakis tetrahedron. This honeycomb is the dual of the triakis truncated tetrahedral honeycomb, with triakis truncated tetrahedral
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
Blue tectosilicate mineral
The silicon and aluminum atoms are located at the corners of a truncated octahedron with the chloride and four sodium atoms inside. (A similar structure
Sodalite
Operation in Euclidean geometry
with a tiling order of 4, for example the tetrahedron {3,3} becoming an octahedron {3,4}. As a special case, a square tiling {4,4} will turn into another
Rectification_(geometry)
Infinite regular skew polyhedron
each vertex (related to bitruncated cubic honeycomb, constructed by truncated octahedron with their square faces removed and linking hole pairs of holes together
Regular_skew_apeirohedron
Official match ball for 2006 FIFA World Cup
14 curved panels (making the ball topologically equivalent to a truncated octahedron), rather than the 32 that have been standard since 1970. Like the
Adidas_Teamgeist
There are two degrees of truncations, including a bitruncation. The truncated 5-cell, truncated pentachoron or truncated 4-simplex is bounded by 10
Truncated_5-cell
Cube that fits through hole in smaller cube
cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron, icosidodecahedron, truncated cuboctahedron, truncated icosahedron, truncated dodecahedron
Prince_Rupert's_cube
Infinite polyhedron with non-planar faces
Im3m [[4,3,4]] 8°:2 *4222 {4,5} 1 truncated octahedron 2 hexagonal prisms I3 [[4,3+,4]] 8°:2 2*42 {3,7} 1 octahedron 1 icosahedron Fd3 [[3[4]]]+ 2°− 3222
Skew_apeirohedron
Polyhedron with 24 faces
In geometry, the great triakis octahedron is the dual of the stellated truncated hexahedron (U19). It has 24 intersecting isosceles triangle faces. Part
Great_triakis_octahedron
Metabiaugmented dodecahedron 23 Triaugmented dodecahedron 24 Truncated cube Truncated octahedron Rhombicuboctahedron Elongated square gyrobicupola Gyroelongated
List of small polyhedra by vertex count
List_of_small_polyhedra_by_vertex_count
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TRUNCATED OCTAHEDRON
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