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Polyhedron with 8 triangles and 6 squares
A cuboctahedron, rectified cube, or rectified octahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices
Cuboctahedron
Archimedean solid with 26 faces
the truncated cuboctahedron or great rhombicuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It has 12 square
Truncated_cuboctahedron
Two joined triangular cupolae
configurations differ. It is also called the anticuboctahedron, twisted cuboctahedron, or disheptahedron. In chemistry, the triangular orthobicupola can be
Triangular_orthobicupola
Polyhedral compromise map projection
by Buckminster Fuller. In 1943, Fuller proposed a projection onto a cuboctahedron, which he called the Dymaxion World, using the name Dymaxion which he
Dymaxion_map
Polyhedron with 20 faces
golden ratio. A regular icosahedron is topologically identical to a cuboctahedron with its 6 square faces bisected on diagonals with pyritohedral symmetry
Icosahedron
Polyhedron with 20 faces
In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons
Cubitruncated_cuboctahedron
Type of polyhedron
The expanded cuboctahedron is a polyhedron constructed by expansion of the cuboctahedron. It has 50 faces: 8 triangles, 30 squares, and 12 rhombs. The
Expanded_cuboctahedron
Archimedean solid with 38 faces
In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and
Snub_cube
called the Conway snub cuboctahedron in but will be confused with the Coxeter snub cuboctahedron, the snub cube. See snub cuboctahedron. The snub rhombicuboctahedron
Snub_rhombicuboctahedron
Catalan solid with 12 faces
vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron. As a parallelohedron, the rhombic dodecahedron can be used to tesselate
Rhombic_dodecahedron
Polyhedron made from triangles that approximates a sphere
A geodesic polyhedron is a convex polyhedron made from triangles which approximates a sphere. They usually have icosahedral symmetry, such that they have
Geodesic_polyhedron
polyhedron with different proportions can be constructed as an augmented cuboctahedron, with a square face augmented by a square pyramid. This construction
Diminished rhombic dodecahedron
Diminished_rhombic_dodecahedron
A hemi-cuboctahedron is an abstract polyhedron, containing half the faces of a semiregular cuboctahedron. It has 4 triangular faces and 3 square faces
Hemi-cuboctahedron
Archimedean solid with 26 faces
The rhombicuboctahedron or small rhombicuboctahedron is a polyhedron with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named
Rhombicuboctahedron
Method of describing higher-order polyhedra
truncated cube, and taC, parsed as t(aC), is (topologically) a truncated cuboctahedron. The simplest operator dual swaps vertex and face elements; e.g., a
Conway_polyhedron_notation
In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces (8 triangles, 6 squares, and 6 octagons), 48 edges
Small_cubicuboctahedron
Polyhedron with 26 faces
In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed
Great_truncated_cuboctahedron
planes) 11 Cuboctahedron (regular) Oh 43 Compound of cube and octahedron (First stellation of cuboctahedron) Oh 44 Second stellation of cuboctahedron Oh 45
List of Wenninger polyhedron models
List_of_Wenninger_polyhedron_models
Isogonal polyhedron with regular faces
discovered the regular dodecahedron before 500 BC.[full citation needed] The cuboctahedron was known by Plato. Archimedes (287 BC – 212 BC) discovered all of the
Uniform_polyhedron
Solid made by joining an n- and 2n-gon with triangles and squares
among the Johnson solids, and can be formed by taking sections of the cuboctahedron, rhombicuboctahedron, and rhombicosidodecahedron, respectively. Cupolae
Cupola_(geometry)
Polyhedra in which all vertices are the same
size. They are the cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron, icosidodecahedron, truncated cuboctahedron, truncated icosahedron
Archimedean_solid
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 at
Truncated_octahedron
Partition of a toroidal surface into polygons
octahedron expanded cuboctahedron truncated cuboctahedron truncated cuboctahedron truncated cuboctahedron truncated cuboctahedron Vertices 32 30 30 62
Toroidal_polyhedron
Natural number
tetrahedra that makes it the simplest of five regular compounds. The cuboctahedron, on the other hand, is a rectified cube or rectified octahedron, and
8
Empirical study of systems in transformation
attached to the doubling and quadrupling of edges that occur, when a cuboctahedron is collapsed through icosahedral, octahedral and tetrahedral stages
Synergetics_(Fuller)
Polyhedral compound
also the first stellation of the cuboctahedron and given as Wenninger model index 43. It can be seen as a cuboctahedron with square and triangular pyramids
Compound of cube and octahedron
Compound_of_cube_and_octahedron
tetrahedral cupola is a polychoron bounded by one tetrahedron, a parallel cuboctahedron, connected by 10 triangular prisms, and 4 triangular pyramids. The tetrahedral
Tetrahedral_cupola
Polyhedral compound
arrangement of this compound is shared by a convex nonuniform truncated cuboctahedron, having rectangular faces, alongside irregular hexagons and octagons
Compound_of_two_snub_cubes
Topics referred to by the same term
exchange, or central office (CO) Cofunction, or Co, in trigonometry Cuboctahedron, a uniform polyhedron Nguyễn Hữu Có (1925–2012), Vietnamese general
CO
Natural number, composite number
three dimensions contain fourteen faces or vertices as facets: The cuboctahedron, one of two quasiregular polyhedra, has 14 faces and is the only uniform
14_(number)
Graph where every edge is in one triangle
graph can be constructed in this way. For instance, the graph of the cuboctahedron is the line graph of a cube, so it is locally linear. The locally linear
Locally_linear_graph
Nonconvex uniform polyhedron with 20 faces
In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48
Great_cubicuboctahedron
Color space
geometry that the OSA finally chose is a rhombohedral lattice based on a cuboctahedron. Each of the twelve vertices of this solid are equal distance from the
OSA-UCS
Catalan solid with 48 faces
Catalan solid with 48 faces and the dual to the Archimedean truncated cuboctahedron. As such it is face-transitive but with irregular face polygons. It
Disdyakis_dodecahedron
Hierarchical outline list of articles related to the physical sciences
the Earth including its atmosphere in Earth sciences and a diamond cuboctahedron in materials science bottom: Maunakea Observatories, group of independent
Outline_of_physical_science
Operation in Euclidean geometry
called a cuboctahedron, and also represented as { 4 3 } {\displaystyle {\begin{Bmatrix}4\\3\end{Bmatrix}}} . And a rectified cuboctahedron rr{4,3} is
Rectification_(geometry)
Type of polyhedron
known as truncated small rhombicuboctahedron or beveled cuboctahedron—is a polyhedron, constructed from a rhombicuboctahedron by truncating
Truncated_rhombicuboctahedron
Shape with six sides
truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron. These hexagons can be considered
Hexagon
Truncated octahedron Tetrahedron/Octahedron 4 3 2 | Truncated cuboctahedron Cube/Cuboctahedron/Octahedron 5 3 2 | Truncated icosidodecahedron
Omnitruncated_polyhedron
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
vertex figure. The cantellated square tiling honeycomb, rr{4,4,3}, has cuboctahedron, square tiling, and triangular prism facets, with an isosceles triangular
Square_tiling_honeycomb
Cupola with hexagonal base
the triangular cupola is a Johnson solid. It can be seen as half a cuboctahedron. The triangular cupola can be applied to construct many polyhedrons
Triangular_cupola
Quasiregular space-filling tesselation
honeycomb. Its Voronoi cell is a rhombic dodecahedron, the dual of the cuboctahedron vertex figure for the tet-oct honeycomb. The D+ 3 packing can be constructed
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
Self-intersecting uniform polyhedron
3⁄2.4.3 3⁄2 3 | 2 Truncated tetrahedron Cantellated tetrahedron (Cuboctahedron) Omnitruncated tetrahedron (Truncated octahedron) Snub tetrahedron
Uniform_star_polyhedron
Removal of alternate vertices
Alternation of a truncated cuboctahedron creates a nonuniform snub cube.
Alternation_(geometry)
Topics referred to by the same term
SM U-20 (Austria-Hungary), a submarine of the Austro-Hungarian Navy Great truncated cuboctahedron Meizu U20, a smartphone Roland U-20, a synthesizer Small nucleolar RNA
U20
Geometric operation which truncates the edges of polyhedra
Goldberg polyhedron GPIV(2,0) or {4+,3}2,0. Its dual is the tetrakis cuboctahedron. A twisty puzzle of the DaYan Gem 7 is the shape of a chamfered cube
Chamfer_(geometry)
Convex polyhedron with regular faces
Pentagonal orthocupolarotunda 34 Pentagonal orthobirotunda gyrobi- Cuboctahedron "Triangular gyrobicupola" 29 Square gyrobicupola 31 Pentagonal gyrobicupola
Johnson_solid
Convex polyhedron projected from hypercube
Minkowski sum of a cube and a truncated octahedron forms the truncated cuboctahedron, while the Minkowski sum of the cube and the rhombic dodecahedron forms
Zonohedron
solid Truncated tetrahedron, Cuboctahedron, Truncated cube, Truncated octahedron, Rhombicuboctahedron, Truncated cuboctahedron, Snub cube, Icosidodecahedron
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Operation that cuts polytope vertices, creating a new facet in place of each vertex
between a full cube and a rectified cube. The final polyhedron is a cuboctahedron. The middle image is the uniform truncated cube; it is represented by
Truncation_(geometry)
solid Truncated tetrahedron Cuboctahedron Truncated cube Truncated octahedron Rhombicuboctahedron Truncated cuboctahedron Snub cube Icosidodecahedron
List_of_mathematical_shapes
dodecahedron, the dual of a truncated cuboctahedron. Four more great circles represent the edges of a cuboctahedron, and the last twelve great circles connect
25 great circles of the spherical octahedron
25_great_circles_of_the_spherical_octahedron
Four-dimensional geometrical object
be dissected by a central cuboctahedron into two tetrahedral cupola. This dissection is analogous to the 3D cuboctahedron being dissected by a central
Runcinated_5-cell
Catalan solid with 30 faces
edge-transitive convex polyhedra, the others being the five Platonic solids, the cuboctahedron, the icosidodecahedron, and the rhombic dodecahedron. The rhombic triacontahedron
Rhombic_triacontahedron
Research of materials
A diamond cuboctahedron showing seven crystallographic planes, imaged with scanning electron microscopy
Materials_science
Geometric operation applied to a polyhedron
, and Coxeter diagram . The snub cuboctahedron is the alternation of the truncated cuboctahedron, t { 4 3 } {\displaystyle
Snub_(geometry)
Polyhedron with 48 faces
isohedral polyhedron. It is the dual of the uniform great truncated cuboctahedron. It has 48 triangular faces. The triangles have one angle of arccos
Great_disdyakis_dodecahedron
Cube that fits through hole in smaller cube
Rupert property: the cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron, icosidodecahedron, truncated cuboctahedron, truncated icosahedron
Prince_Rupert's_cube
Rules to predict ionic compounds' crystal structures
octahedron 0.414 7 capped octahedron 0.592 8 square antiprism (anticube) 0.645 8 cube 0.732 9 triaugmented triangular prism 0.732 12 cuboctahedron 1.00
Pauling's_rules
Topics referred to by the same term
may refer to: Tetrakis (Paphlagonia), an ancient Greek city Tetrakis cuboctahedron, convex polyhedron with 32 triangular faces Tetrakis hexahedron, an
Tetrakis
a compact uniform honeycomb, constructed from cube, octahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring
Cubic-octahedral_honeycomb
Existence of antipodal pairs in covers of spheres
the closures of the red, yellow, and blue areas, in the pattern of a cuboctahedron. The red and yellow sets do not contain any antipodal pairs (each red
Lusternik–Schnirelmann theorem
Lusternik–Schnirelmann_theorem
more complicated cell. Each edge of the cuboctahedron represents a peripheral Au–Au bond. The cuboctahedron has 24 edges while the icosahedron has 30
Gold_cluster
Four-dimensional analogue of the cube
including the four-dimensional tesseract and 24-cell, the three-dimensional cuboctahedron, and the two-dimensional hexagon. In particular, the tesseract is the
Tesseract
Geometric figure
4-face types t1{33} t0,2{33} t0,3{33} Cell types Tetrahedron Octahedron Cuboctahedron Triangular prism Vertex figure triangular elongated-antiprismatic prism
5-cell_honeycomb
Any of the five regular polyhedra
next most regular convex polyhedra after the Platonic solids are the cuboctahedron, which is a rectification of the cube and the octahedron, and the icosidodecahedron
Platonic_solid
Nonconvex uniform polyhedron with 26 faces
with the convex great rhombicuboctahedron, also called the truncated cuboctahedron. An alternative name for this figure is quasirhombicuboctahedron. From
Nonconvex great rhombicuboctahedron
Nonconvex_great_rhombicuboctahedron
Structural design made of isolated members held in place by tension
coordinates lie along a continuous family of positions ranging from the cuboctahedron to the octahedron (as limit cases), which are linked by a helical
Tensegrity
truncated cuboctahedron into 2 dimensions. Thus, the omnitruncated tesseract may be thought of as another analogue of the truncated cuboctahedron in 4 dimensions
Runcinated_tesseracts
Polyhedron resulting from the snub operation
are obtained by snubification of the truncated octahedron, truncated cuboctahedron and the truncated icosidodecahedron - the three convex truncated quasiregular
Snub_polyhedron
polyhedra, created by inserting two squares into the vertex figures of the Cuboctahedron and Icosidodecahedron. Coxeter, H. S. M.; Longuet-Higgins, M. S.; Miller
List of uniform polyhedra by vertex figure
List_of_uniform_polyhedra_by_vertex_figure
Archimedean solid with 32 faces
holographic icosidodecahedra joined at the midpoints of their segments. Cuboctahedron Great truncated icosidodecahedron Icosahedron Rhombicosidodecahedron
Icosidodecahedron
44th Johnson solid (26 faces)
a triangular bicupola (either triangular orthobicupola, J27, or the cuboctahedron) by inserting a hexagonal antiprism between its congruent halves. A
Gyroelongated triangular bicupola
Gyroelongated_triangular_bicupola
State of matter
A diamond cuboctahedron showing seven crystallographic planes, imaged with scanning electron microscopy
Solid
Polytope or tiling whose vertices are identical
3.8.8 A distorted hexagonal prism (ditrigonal trapezoprism) A distorted rhombicuboctahedron A shallow truncated cuboctahedron A hyper-truncated cube
Isogonal_figure
Polyhedron with 7 faces
quadrilateral. It is 2-covered by the cuboctahedron, meaning that it has the same abstract vertex figure as a cuboctahedron wherein each vertex is surrounded
Tetrahemihexahedron
Number of atoms, molecules or ions bonded to a molecule or crystal
same plane and 3 above and below and the coordination polyhedron is a cuboctahedron. α-Iron has a body centered cubic structure where each iron atom has
Coordination_number
Partition of a sphere's surface into polygons
family). All the hemisphere tilings arise from either the octahedron, cuboctahedron, icosidodecahedron, or a single ( n , 2 ) {\displaystyle (n,2)} dihedral
Spherical_polyhedron
Ordered arrangement of atoms, ions, or molecules in a crystalline material
Body-centered cubic (BCC) 0.68 8 (Cube) Face-centered cubic (FCC) 0.74 12 (Cuboctahedron) Hexagonal close-packed (HCP) 0.74 12 (Triangular orthobicupola)
Crystal_structure
Extending the elements of a polytope to form a new figure
For example the cube is not usually considered a stellation of the cuboctahedron. Generalising Miller's rules there are: 4 stellations of the rhombic
Stellation
The truncated cuboctahedron, a zero-symmetric polyhedron
Zero-symmetric_graph
Class of chemical substance
O'Keeffe M, Yaghi OM (2001). "Porous Metal-Organic Polyhedra: 25 Å Cuboctahedron Constructed from 12 Cu2(CO2)4 Paddle-Wheel Building Blocks". Journal
Metal–organic_framework
Color
golden necklace from Färjestaden; the Wikipedia logo in gold; A golden cuboctahedron; A fountain pen with a gilded nib. Common connotations First place in
Gold_(color)
arccos ( − 1 3 ) {\displaystyle \arccos(-{\frac {1}{3}})} 109.471° Cuboctahedron r{3,4} (3.4.3.4) arccos ( − 3 3 ) {\displaystyle \arccos(-{\frac {\sqrt
Table of polyhedron dihedral angles
Table_of_polyhedron_dihedral_angles
was chosen so that its circumcircle lies on the intersphere of the cuboctahedron, which also becomes the intersphere of the dual rhombic dodecahedron
Dual_uniform_polyhedron
Topics referred to by the same term
In geometry, this may refer to: Truncated cuboctahedron - an Archimedean solid, with Schläfli symbol tr{4,3}, and Coxeter diagram . Nonconvex great rhombicuboctahedron
Great_rhombicuboctahedron
All Latin and Greek roots beginning with G
ctenidium, ctenoid, Ctenophora cub- cube Greek κύβος (kúbos) cubic, cuboctahedron, cuboid, hemicube, hypercube cub- lie Latin cubare incubation, succuba
List of Greek and Latin roots in English/A–G
List_of_Greek_and_Latin_roots_in_English/A–G
Tabletop game that loosely simulates football
with actual kicking feet; it uses a ball that is not a sphere but a cuboctahedron, to limit rolling distance and bring it to a firm stop even if the table
Tabletop_football
Cell structure involved in protein transport
Sec13/31 complexes to form a cuboctahedron with a broader lattice than its Clathrin vesicle analog. The formation of the cuboctahedron deforms the ER membrane
COPII
Coordinate system
(1,1,1,0), and for the cube, octahedron, rhombic dodecahedron and cuboctahedron of volumes 3, 4, 6 and 20 respectively, given the starting tetrahedron
Quadray_coordinates
pattern p.q.r.q. The name rhombic stems from inserting a square in the cuboctahedron and icosidodecahedron. The Wythoff symbol is of the form p q|r. These
List of uniform polyhedra by Wythoff symbol
List_of_uniform_polyhedra_by_Wythoff_symbol
Polyhedron with two kinds of faces
quasiregular. There are only two convex quasiregular polyhedra: the cuboctahedron and the icosidodecahedron. Their names, given by Kepler, come from recognizing
Quasiregular_polyhedron
Polyhedron with 12 faces
with twelve rhombic faces and octahedral symmetry. It is dual to the cuboctahedron, an Archimedean solid, and occurs in nature as a crystal form. The rhombic
Dodecahedron
octahedron 4.6.6 2 4 | 3 Oh C20 W007 U08 K13 24 36 14 6{4} +8{6} Truncated cuboctahedron 4.6.8 2 3 4 | Oh C23 W015 U11 K16 48 72 26 12{4} +8{6} +6{8} Truncated
List_of_uniform_polyhedra
Topics referred to by the same term
Austro-Hungarian Navy Bugatti U-16, an automobile engine Cubitruncated cuboctahedron Small nucleolar RNA SNORD16 Uint16_t, a 16-bit unsigned integer Uppland
U16
Geometric pattern used in art
Polyhedra in stereographic projection Octahedron Cuboctahedron Icosidodecahedron
Overlapping_circles_grid
Polyhedron with 10 faces
visible. It shares the vertex arrangement and edge arrangement with the cuboctahedron (having the square faces in common), and with the octahemioctahedron
Cubohemioctahedron
Regular tiling of hyperbolic 3-space
rectified order-5 cubic honeycomb, , has alternating icosahedron and cuboctahedron cells, with a pentagonal prism vertex figure. There are four rectified
Order-5_cubic_honeycomb
Self-intersecting polyhedron with 12 faces
stellation of the rhombic dodecahedron include the 12 vertices of the cuboctahedron, together with eight additional vertices (the degree-3 vertices of the
First stellation of the rhombic dodecahedron
First_stellation_of_the_rhombic_dodecahedron
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CUBOCTAHEDRON
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