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93 relations: Abstract polytope, Archimedean graph, Archimedean solid, Archimedes, Bicupola (geometry), Buckminster Fuller, By Any Other Name, Cantellation (geometry), Cartesian coordinate system, Conformal map, Convex uniform honeycomb, Covering space, Coxeter element, CRC Press, Cross section (geometry), Cube, Cubic honeycomb, Cubohemioctahedron, Dover Publications, Dual polyhedron, Dymaxion, Dymaxion map, Edge (geometry), Elite (video game), Facet (geometry), Fundamental domain, Geometry, Graph theory, Gyrobifastigium, Hamiltonian path, Hero of Alexandria, Hexagon, Hyperbolic space, Icosahedron, Icosidodecahedron, Isogonal figure, Isotoxal figure, Johnson solid, Mathematics, N-skeleton, Norman Johnson (mathematician), Octahedron, Octahemioctahedron, Orbifold notation, Orthant, Orthographic projection, Oxford University Press, Plato, Polyhedron, Polytope, ..., Polytope compound, Projection (linear algebra), Quartic graph, Quasiregular polyhedron, Rectification (geometry), Rectified 24-cell, Regular graph, Regular Polytopes (book), Rhombic dodecahedron, Rhombicuboctahedron, Simple Lie group, Sphere, Sphere packing, Spherical polyhedron, Square, Square pyramid, Star Trek, Starship Enterprise, Stellation, Stereographic projection, Symmetry group, Tessellation, Tesseract, Tesseractic honeycomb, Tetradecahedron, Tetrahedral-octahedral honeycomb, Tetrahedron, Tetrahemihexahedron, Triangle, Triangular cupola, Triangular orthobicupola, Truncated cuboctahedron, Uniform 4-polytope, Uniform star polyhedron, Vertex (geometry), Vertex (graph theory), Vertex configuration, Vertex figure, Wythoff construction, Wythoff symbol, 16-cell, 24-cell, 24-cell honeycomb. Expand index (43 more) »
Abstract polytope
In mathematics, an abstract polytope is an algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope, but not any purely geometric properties such as angles, edge lengths, etc.
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Archimedean graph
In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids.
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Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.
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Archimedes
Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.
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Bicupola (geometry)
In geometry, a bicupola is a solid formed by connecting two cupolae on their bases.
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Buckminster Fuller
Richard Buckminster "Bucky" Fuller (July 12, 1895 – July 1, 1983) was an American architect, systems theorist, author, designer, inventor and futurist.
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By Any Other Name
"By Any Other Name" is a second season episode of the American science fiction television series Star Trek, first broadcast February 23, 1968, and repeated May 31, 1968.
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Cantellation (geometry)
In geometry, a cantellation is an operation in any dimension that bevels a regular polytope at its edges and vertices, creating a new facet in place of each edge and vertex.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
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Convex uniform honeycomb
In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Coxeter element
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
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CRC Press
The CRC Press, LLC is a publishing group based in the United States that specializes in producing technical books.
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Cross section (geometry)
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces.
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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Cubic honeycomb
The cubic honeycomb or cubic cellulation is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of cubic cells.
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Cubohemioctahedron
In geometry, the cubohemioctahedron is a nonconvex uniform polyhedron, indexed as U15.
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Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
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Dual polyhedron
In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.
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Dymaxion
Dymaxion is a term that Buckminster Fuller associated with much of his work—prominently his Dymaxion house and Dymaxion car.
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Dymaxion map
The Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron, which can be unfolded and flattened to two dimensions.
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Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
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Elite (video game)
Elite is a space trading video game, written and developed by David Braben and Ian Bell and originally published by Acornsoft for the BBC Micro and Acorn Electron computers in September 1984.
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Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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Fundamental domain
Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
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Gyrobifastigium
In geometry, the gyrobifastigium is the 26th Johnson solid (J26).
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Hamiltonian path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.
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Hero of Alexandria
Hero of Alexandria (ἭρωνGenitive: Ἥρωνος., Heron ho Alexandreus; also known as Heron of Alexandria; c. 10 AD – c. 70 AD) was a mathematician and engineer who was active in his native city of Alexandria, Roman Egypt.
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Hexagon
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
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Hyperbolic space
In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.
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Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
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Icosidodecahedron
In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces.
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Isogonal figure
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.
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Isotoxal figure
In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.
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Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism, or antiprism), and each face of which is a regular polygon.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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N-skeleton
In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.
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Norman Johnson (mathematician)
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
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Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
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Octahemioctahedron
In geometry, the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U3.
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Orbifold notation
In geometry, orbifold notation (or orbifold signature) is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.
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Orthant
In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions.
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Orthographic projection
Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.
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Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
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Plato
Plato (Πλάτων Plátōn, in Classical Attic; 428/427 or 424/423 – 348/347 BC) was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world.
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
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Polytope compound
A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.
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Projection (linear algebra)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
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Quartic graph
In the mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4.
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Quasiregular polyhedron
In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.
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Rectification (geometry)
In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.
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Rectified 24-cell
In geometry, the rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells: 24 cubes, and 24 cuboctahedra.
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Regular graph
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.
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Regular Polytopes (book)
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
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Rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.
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Rhombicuboctahedron
In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces.
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Simple Lie group
In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
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Spherical polyhedron
In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.
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Square
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.
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Square pyramid
In geometry, a square pyramid is a pyramid having a square base.
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Star Trek
Star Trek is an American media franchise based on the science fiction television series created by Gene Roddenberry.
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Starship Enterprise
Enterprise or USS Enterprise (often referred to as the "Starship Enterprise") is the name of several fictional spacecraft, some of which are the main craft and setting for various television series and films in the Star Trek science fiction franchise.
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Stellation
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.
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Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
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Symmetry group
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
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Tessellation
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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Tesseract
In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.
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Tesseractic honeycomb
In four-dimensional euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol, and constructed by a 4-dimensional packing of tesseract facets.
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Tetradecahedron
A tetradecahedron with ''D2d'' symmetry, existing in the Weaire–Phelan structure A tetradecahedron is a polyhedron with 14 faces.
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Tetrahedral-octahedral honeycomb
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Tetrahemihexahedron
In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Triangular cupola
In geometry, the triangular cupola is one of the Johnson solids (J3).
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Triangular orthobicupola
In geometry, the triangular orthobicupola is one of the Johnson solids (J27).
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Truncated cuboctahedron
In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.
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Uniform 4-polytope
In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
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Uniform star polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.
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Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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Vertex (graph theory)
In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
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Vertex configuration
In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
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Wythoff symbol
In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle.
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16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
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24-cell
In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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24-cell honeycomb
In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean space by regular 24-cells.
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Cantellated 3-simplex, Cantellated tetrahedron, Co (geometry), Cubeoctahedron, Cubo-octahedron, Cubocta, Cuboctahedra, Cuboctahedral graph, Expanded 3-simplex, Expanded tetrahedron, Heptaparallelohedron, Rectified 3-cube, Rectified 3-orthoplex, Rectified cube, Rectified octahedron, Rhombitetratetrahedron, Small Cuboctahedron, Small rhombitetratetrahedron, Triangular gyrobicupola, Trigonal gyrobicupola, Vector equilibrium.
References
[1] https://en.wikipedia.org/wiki/Cuboctahedron
