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48 relations: Bipyramid, Catalan solid, Convex uniform honeycomb, Cross-polytope, Cubic honeycomb, Delaunay triangulation, Deltahedron, Disdyakis dodecahedron, Disdyakis triacontahedron, Dual polyhedron, Facet (geometry), Geometry, Gyroelongated bipyramid, Gyroelongated square bipyramid, Icosahedron, Johnson solid, List of convex uniform tilings, Octahedron, Pentagonal bipyramid, Pentakis dodecahedron, Planar graph, Platonic solid, Polygon, Polyhedron, Polytope, Regular 4-polytope, Simple polytope, Simplex, Simplicial complex, Snub disphenoid, Steinitz's theorem, Tetragonal disphenoid honeycomb, Tetrahedral-octahedral honeycomb, Tetrahedron, Tetrakis hexahedron, Tetrakis square tiling, Triakis icosahedron, Triakis octahedron, Triakis tetrahedron, Triangular bipyramid, Triangular tiling, Triaugmented triangular prism, Truncated hexagonal tiling, Truncated trihexagonal tiling, 16-cell, 4-polytope, 5-cell, 600-cell.
Bipyramid
An n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal pyramid and its mirror image base-to-base.
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Catalan solid
In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid.
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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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Cross-polytope
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.
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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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Delaunay triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P).
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Deltahedron
In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles.
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Disdyakis dodecahedron
In geometry, a disdyakis dodecahedron, (also hexoctahedron, hexakis octahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron), is a Catalan solid with 48 faces and the dual to the Archimedean truncated cuboctahedron.
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Disdyakis triacontahedron
In geometry, a disdyakis triacontahedron, hexakis icosahedron, decakis dodecahedron or kisrhombic triacontahedron is a Catalan solid with 120 faces and the dual to the Archimedean truncated icosidodecahedron.
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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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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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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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Gyroelongated bipyramid
In geometry, the gyroelongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid by inserting an n-gonal antiprism between its congruent halves.
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Gyroelongated square bipyramid
In geometry, the gyroelongated square bipyramid or heccaidecadeltahedron is one of the Johnson solids (J17).
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Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
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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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List of convex uniform tilings
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings.
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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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Pentagonal bipyramid
In geometry, the pentagonal bipyramid (or dipyramid) is third of the infinite set of face-transitive bipyramids.
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Pentakis dodecahedron
In geometry, a pentakis dodecahedron or kisdodecahedron is a dodecahedron with a pentagonal pyramid covering each face; that is, it is the Kleetope of the dodecahedron.
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Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.
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Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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Polygon
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
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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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Regular 4-polytope
In mathematics, a regular 4-polytope is a regular four-dimensional polytope.
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Simple polytope
In geometry, a d-dimensional simple polytope is a d-dimensional polytope each of whose vertices are adjacent to exactly d edges (also d facets).
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Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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Simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).
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Snub disphenoid
In geometry, the snub disphenoid, Siamese dodecahedron, triangular dodecahedron or dodecadeltahedron is a three-dimensional convex polyhedron with twelve equilateral triangles as its faces.
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Steinitz's theorem
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the (simple) 3-vertex-connected planar graphs (with at least four vertices).
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Tetragonal disphenoid honeycomb
The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of identical tetragonal disphenoidal cells.
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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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Tetrakis hexahedron
In geometry, a tetrakis hexahedron (also known as a tetrahexahedron, hextetrahedron, tetrakis cube, and kiscube) is a Catalan solid.
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Tetrakis square tiling
In geometry, the tetrakis square tiling is a tiling of the Euclidean plane.
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Triakis icosahedron
In geometry, the triakis icosahedron (or kisicosahedron) is an Archimedean dual solid, or a Catalan solid.
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Triakis octahedron
In geometry, a triakis octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid.
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Triakis tetrahedron
In geometry, a triakis tetrahedron (or kistetrahedron) is an Archimedean dual solid, or a Catalan solid.
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Triangular bipyramid
In geometry, the triangular bipyramid (or dipyramid) is a type of hexahedron, being the first in the infinite set of face-transitive bipyramids.
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Triangular tiling
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.
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Triaugmented triangular prism
In geometry, the triaugmented triangular prism or tetracaidecadeltahedron is one of the Johnson solids (J51).
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Truncated hexagonal tiling
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.
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Truncated trihexagonal tiling
In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane.
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16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
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4-polytope
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.
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5-cell
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
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600-cell
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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References
[1] https://en.wikipedia.org/wiki/Simplicial_polytope
