Table of Contents
48 relations: Abstract polytope, Binomial coefficient, Closed set, Convex polytope, Convex uniform honeycomb, Cube, Cubic honeycomb, Dodecahedron, Domain (mathematical analysis), Edge (geometry), Euclidean plane, Euler characteristic, Face (geometry), Facet (geometry), Graduate Texts in Mathematics, Half-space (geometry), Kepler–Poinsot polyhedron, Line segment, Merriam-Webster, Norman Johnson (mathematician), Order-4 dodecahedral honeycomb, Order-5 square tiling, Pentagram, Petrie polygon, Platonic solid, Polygon, Polyhedral combinatorics, Polyhedron, Polytope, Regular 4-polytope, Schläfli symbol, Set theory, Simplex, Small stellated dodecahedron, Solid geometry, Square, Square tiling, Star polyhedron, Surface, Tessellation, Tesseract, Uniform tiling, Vertex (geometry), Vertex figure, Webster's Dictionary, 120-cell, 4-polytope, 5-polytope.
- Planar surfaces
Abstract polytope
In mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely geometric properties such as points and lines.
See Face (geometry) and Abstract polytope
Binomial coefficient
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem.
See Face (geometry) and Binomial coefficient
Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
See Face (geometry) and Closed set
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Face (geometry) and convex polytope are convex geometry.
See Face (geometry) and Convex polytope
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.
See Face (geometry) and Convex uniform honeycomb
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces.
Cubic honeycomb
The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells.
See Face (geometry) and Cubic honeycomb
Dodecahedron
In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces.
See Face (geometry) and Dodecahedron
Domain (mathematical analysis)
In mathematical analysis, a domain or region is a non-empty, connected, and open set in a topological space, in particular any non-empty connected open subset of the real coordinate space or the complex coordinate space.
See Face (geometry) and Domain (mathematical analysis)
Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. Face (geometry) and edge (geometry) are elementary geometry.
See Face (geometry) and Edge (geometry)
Euclidean plane
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.
See Face (geometry) and Euclidean plane
Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
See Face (geometry) and Euler characteristic
Face (geometry)
In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron. Face (geometry) and face (geometry) are convex geometry, elementary geometry, planar surfaces and polyhedra.
See Face (geometry) and Face (geometry)
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. Face (geometry) and facet (geometry) are polyhedra.
See Face (geometry) and Facet (geometry)
Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
See Face (geometry) and Graduate Texts in Mathematics
Half-space (geometry)
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.
See Face (geometry) and Half-space (geometry)
Kepler–Poinsot polyhedron
In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
See Face (geometry) and Kepler–Poinsot polyhedron
Line segment
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. Face (geometry) and line segment are elementary geometry.
See Face (geometry) and Line segment
Merriam-Webster
Merriam-Webster, Incorporated is an American company that publishes reference books and is mostly known for its dictionaries.
See Face (geometry) and Merriam-Webster
Norman Johnson (mathematician)
Norman Woodason Johnson was a mathematician at Wheaton College, Norton, Massachusetts.
See Face (geometry) and Norman Johnson (mathematician)
Order-4 dodecahedral honeycomb
In hyperbolic geometry, the order-4 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) of hyperbolic 3-space.
See Face (geometry) and Order-4 dodecahedral honeycomb
Order-5 square tiling
In geometry, the order-5 square tiling is a regular tiling of the hyperbolic plane.
See Face (geometry) and Order-5 square tiling
Pentagram
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon.
See Face (geometry) and Pentagram
Petrie polygon
In geometry, a Petrie polygon for a regular polytope of dimensions is a skew polygon in which every consecutive sides (but no) belongs to one of the facets.
See Face (geometry) and Petrie polygon
Platonic solid
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.
See Face (geometry) and Platonic solid
Polygon
In geometry, a polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
See Face (geometry) and Polygon
Polyhedral combinatorics
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.
See Face (geometry) and Polyhedral combinatorics
Polyhedron
In geometry, a polyhedron (polyhedra or polyhedrons) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. Face (geometry) and polyhedron are polyhedra.
See Face (geometry) and Polyhedron
Polytope
In elementary geometry, a polytope is a geometric object with flat sides (faces).
See Face (geometry) and Polytope
Regular 4-polytope
In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope.
See Face (geometry) and Regular 4-polytope
Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations.
See Face (geometry) and Schläfli symbol
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.
See Face (geometry) and Set theory
Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
See Face (geometry) and Simplex
Small stellated dodecahedron
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.
See Face (geometry) and Small stellated dodecahedron
Solid geometry
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space).
See Face (geometry) and Solid geometry
Square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90-degree angles, π/2 radian angles, or right angles).
See Face (geometry) and Square
Square tiling
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. Face (geometry) and square tiling are polyhedra.
See Face (geometry) and Square tiling
Star polyhedron
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. Face (geometry) and star polyhedron are polyhedra.
See Face (geometry) and Star polyhedron
Surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space.
See Face (geometry) and Surface
Tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. Face (geometry) and tessellation are polyhedra.
See Face (geometry) and Tessellation
Tesseract
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube.
See Face (geometry) and Tesseract
Uniform tiling
In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.
See Face (geometry) and Uniform tiling
Vertex (geometry)
In geometry, a vertex (vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect.
See Face (geometry) and Vertex (geometry)
Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off. Face (geometry) and vertex figure are polyhedra.
See Face (geometry) and Vertex figure
Webster's Dictionary
Webster's Dictionary is any of the English language dictionaries edited in the early 19th century by Noah Webster (1758–1843), an American lexicographer, as well as numerous related or unrelated dictionaries that have adopted the Webster's name in his honor.
See Face (geometry) and Webster's Dictionary
120-cell
In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
See Face (geometry) and 120-cell
4-polytope
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.
See Face (geometry) and 4-polytope
5-polytope
In geometry, a five-dimensional polytope (or 5-polytope or polyteron) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which share a polyhedral cell.
See Face (geometry) and 5-polytope
See also
Planar surfaces
- Annulus (mathematics)
- Disk (mathematics)
- Face (geometry)
- Polygons
- Triangle geometry
References
Also known as 10-face, 2-face, 3-face, 3FACE, 4-face, 5-face, 6-face, 7-face, 8-face, 9-face, Cell (geometry), Cell (mathematics), Face (mathematics), Faces (geometry), Hedra, Hypercell, Hypercell (geometry), Hyperface, K-face, Peak (geometry), Peak (mathematics), Polygonal face, Polyhedron face, Polytope face, Ridge (geometry), Ridge (mathematics), Teron (geometry).