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Rhombic triacontahedron, the Glossary

Index Rhombic triacontahedron

The rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces.[1]

Table of Contents

  1. 44 relations: Archimedean solid, Cambridge University Press, Catalan solid, Chamfered dodecahedron, Compound of five cubes, Convex polytope, Coxeter group, Cube, Cuboctahedron, Dual polyhedron, Edge (geometry), Face (geometry), Golden ratio, Golden rhombus, Group action, Icosidodecahedron, Inscribed sphere, Inverse trigonometric functions, Isohedral figure, Isotoxal figure, Octahedron, Penrose tiling, Platonic solid, Polyhedron, Radius, Reflection (mathematics), Regular dodecahedron, Regular icosahedron, Rhombic dodecahedron, Rhombille tiling, Rhombus, Roger von Oech, Role-playing, Rotation, Stephen Wolfram, Symmetry group, Tangent, Tetrahedron, Trigonal trapezohedron, Truncated octahedron, Vertex (geometry), Wolfram Demonstrations Project, WolframAlpha, Zonohedron.

  2. Catalan solids
  3. Quasiregular polyhedra
  4. Zonohedra

Archimedean solid

In geometry, an Archimedean solid is one of 13 convex polyhedra whose faces are regular polygons and whose vertices are all symmetric to each other.

See Rhombic triacontahedron and Archimedean solid

Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

See Rhombic triacontahedron and Cambridge University Press

Catalan solid

In mathematics, a Catalan solid, or Archimedean dual, is a polyhedron that is dual to an Archimedean solid. Rhombic triacontahedron and Catalan solid are Catalan solids.

See Rhombic triacontahedron and Catalan solid

Chamfered dodecahedron

In geometry, the chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons.

See Rhombic triacontahedron and Chamfered dodecahedron

Compound of five cubes

The compound of five cubes is one of the five regular polyhedral compounds.

See Rhombic triacontahedron and Compound of five cubes

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.

See Rhombic triacontahedron and Convex polytope

Coxeter group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).

See Rhombic triacontahedron and Coxeter group

Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces. Rhombic triacontahedron and cube are zonohedra.

See Rhombic triacontahedron and Cube

Cuboctahedron

A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. Rhombic triacontahedron and cuboctahedron are Quasiregular polyhedra.

See Rhombic triacontahedron and Cuboctahedron

Dual polyhedron

In geometry, every polyhedron is associated with a second dual structure, 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.

See Rhombic triacontahedron and Dual polyhedron

Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

See Rhombic triacontahedron and Edge (geometry)

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.

See Rhombic triacontahedron and Face (geometry)

Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

See Rhombic triacontahedron and Golden ratio

Golden rhombus

In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio: Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle.

See Rhombic triacontahedron and Golden rhombus

Group action

In mathematics, many sets of transformations form a group under function composition; for example, the rotations around a point in the plane.

See Rhombic triacontahedron and Group action

Icosidodecahedron

In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces. Rhombic triacontahedron and icosidodecahedron are Quasiregular polyhedra.

See Rhombic triacontahedron and Icosidodecahedron

Inscribed sphere

In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.

See Rhombic triacontahedron and Inscribed sphere

Inverse trigonometric functions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).

See Rhombic triacontahedron and Inverse trigonometric functions

Isohedral figure

In geometry, a tessellation of dimension (a plane tiling) or higher, or a polytope of dimension (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same.

See Rhombic triacontahedron and Isohedral figure

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.

See Rhombic triacontahedron and Isotoxal figure

Octahedron

In geometry, an octahedron (octahedra or octahedrons) is a polyhedron with eight faces.

See Rhombic triacontahedron and Octahedron

Penrose tiling

A Penrose tiling is an example of an aperiodic tiling.

See Rhombic triacontahedron and Penrose tiling

Platonic solid

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.

See Rhombic triacontahedron and Platonic solid

Polyhedron

In geometry, a polyhedron (polyhedra or polyhedrons) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.

See Rhombic triacontahedron and Polyhedron

Radius

In classical geometry, a radius (radii or radiuses) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

See Rhombic triacontahedron and Radius

Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

See Rhombic triacontahedron and Reflection (mathematics)

Regular dodecahedron

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex.

See Rhombic triacontahedron and Regular dodecahedron

Regular icosahedron

In geometry, the regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points onto the cube.

See Rhombic triacontahedron and Regular icosahedron

Rhombic dodecahedron

In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. Rhombic triacontahedron and rhombic dodecahedron are Catalan solids, Quasiregular polyhedra and zonohedra.

See Rhombic triacontahedron and Rhombic dodecahedron

Rhombille tiling

In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Rhombic triacontahedron and rhombille tiling are Quasiregular polyhedra.

See Rhombic triacontahedron and Rhombille tiling

Rhombus

In plane Euclidean geometry, a rhombus (rhombi or rhombuses) is a quadrilateral whose four sides all have the same length.

See Rhombic triacontahedron and Rhombus

Roger von Oech

Roger von Oech (born February 16, 1948) is an American speaker, conference organizer, author, and toy-maker whose focus has been on the study of creativity.

See Rhombic triacontahedron and Roger von Oech

Role-playing

Role-playing or roleplaying is the changing of one's behaviour to assume a role, either unconsciously to fill a social role, or consciously to act out an adopted role.

See Rhombic triacontahedron and Role-playing

Rotation

Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation.

See Rhombic triacontahedron and Rotation

Stephen Wolfram

Stephen Wolfram (born 29 August 1959) is a British-American computer scientist, physicist, and businessman.

See Rhombic triacontahedron and Stephen Wolfram

Symmetry group

In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition.

See Rhombic triacontahedron and Symmetry group

Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point.

See Rhombic triacontahedron and Tangent

Tetrahedron

In geometry, a tetrahedron (tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices.

See Rhombic triacontahedron and Tetrahedron

Trigonal trapezohedron

In geometry, a trigonal trapezohedron is a polyhedron with six congruent quadrilateral faces, which may be scalene or rhomboid. Rhombic triacontahedron and trigonal trapezohedron are zonohedra.

See Rhombic triacontahedron and Trigonal trapezohedron

Truncated octahedron

In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. Rhombic triacontahedron and truncated octahedron are zonohedra.

See Rhombic triacontahedron and Truncated octahedron

Vertex (geometry)

In geometry, a vertex (vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect.

See Rhombic triacontahedron and Vertex (geometry)

Wolfram Demonstrations Project

The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-sized) interactive programmes called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.

See Rhombic triacontahedron and Wolfram Demonstrations Project

WolframAlpha

WolframAlpha is an answer engine developed by Wolfram Research.

See Rhombic triacontahedron and WolframAlpha

Zonohedron

In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon). Rhombic triacontahedron and zonohedron are zonohedra.

See Rhombic triacontahedron and Zonohedron

See also

Catalan solids

Quasiregular polyhedra

Zonohedra

References

[1] https://en.wikipedia.org/wiki/Rhombic_triacontahedron

Also known as 30-hedron, Rhombic 30-hedron, Rhombic triacontahedral, Triacontahedron.