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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. [1]

Alternation (geometry)

In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.

Bisection

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

Dodecagonal prism

In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.

Elongated triangular tiling

In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane.

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.

Great dirhombicosidodecahedron

In geometry, the great dirhombicosidodecahedron is a nonconvex uniform polyhedron, indexed last as U75.

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 &ndash; March 31, 2003) was a British-born Canadian geometer.

Hexagonal antiprism

In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

Hexagonal prism

In geometry, the hexagonal prism is a prism with hexagonal base.

Incenter

In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale.

Kaleidoscope

A kaleidoscope is an optical instrument with two or more reflecting surfaces tilted to each other in an angle, so that one or more (parts of) objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end, due to repeated reflection.

Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

Schwarz triangle

In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere, possibly overlapping, through reflections in its edges.

Snub (geometry)

In geometry, a snub is an operation applied to a polyhedron.

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").

Spherical trigonometry

Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.

Square tiling

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.

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.

Triangular tiling

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.

Truncated square tiling

In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex.

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.

Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

Uniform tiling

In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.

Willem Abraham Wythoff

Willem Abraham Wythoff, born Wijthoff, (6 October 1865 – 21 May 1939) was a Dutch mathematician.

Wythoff symbol

In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle.

References

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