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Rhombic triacontahedron

Index Rhombic triacontahedron

In geometry, 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]

47 relations: Archimedean solid, Cambridge University Press, Catalan solid, Chamfered dodecahedron, Convex hull, Convex polytope, Coxeter element, Coxeter group, Cube, Cuboctahedron, Dodecahedron, Dual polyhedron, Edge (geometry), Face (geometry), Geometry, Golden ratio, Golden rhombus, Group action, Icosahedron, Icosidodecahedron, Inscribed sphere, Isohedral figure, Isotoxal figure, Octahedron, Penrose tiling, Platonic solid, 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 Alpha, Wolfram Demonstrations Project, Zonohedron, 6-cube.

Archimedean solid

In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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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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Chamfered dodecahedron

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

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Convex hull

In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.

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Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

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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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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).

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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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Cuboctahedron

In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.

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Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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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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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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Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

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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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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.

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Golden rhombus

In geometry, a golden rhombus is a rhombus whose diagonals are in the ratio \frac.

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Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

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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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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.

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Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.

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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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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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Penrose tiling

A Penrose tiling is an example of non-periodic tiling generated by an aperiodic set of prototiles.

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Platonic solid

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

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Radius

In classical geometry, a radius 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.

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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.

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Regular dodecahedron

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

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Regular icosahedron

In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices.

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Rhombic dodecahedron

In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.

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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.

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Rhombus

In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.

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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.

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Role-playing

Role-playing 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.

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Rotation

A rotation is a circular movement of an object around a center (or point) of rotation.

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Stephen Wolfram

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

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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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Tangent

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

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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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Trigonal trapezohedron

In geometry, a trigonal trapezohedron or trigonal deltohedron is a three-dimensional figure formed by six congruent rhombi.

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Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

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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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Wolfram Alpha

Wolfram Alpha (also styled WolframAlpha, and Wolfram|Alpha) is a computational knowledge engine or answer engine developed by Wolfram Alpha LLC, a subsidiary of Wolfram Research.

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Wolfram Demonstrations Project

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

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Zonohedron

A zonohedron is a convex polyhedron with point symmetry, every face of which is a polygon with point symmetry.

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6-cube

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

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Redirects here:

30-hedron, Rhombic 30-hedron, Rhombic triacontahedral, Triacontahedron.

References

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

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