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Dodecahedron

Index Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces. [1]

86 relations: Archimedean solid, Bilinski dodecahedron, Cobaltite, Compound of two icosahedra, Convex hull, Convex set, Conway polyhedron notation, Coxeter–Dynkin diagram, Crystal habit, Crystallographic point group, Crystallography, Cube, Cubic crystal system, Cuboctahedron, Cupola (geometry), Cyclic group, Decagonal prism, Dihedral group, Dodecahedron, Dual polyhedron, Edge (geometry), Elongated dodecahedron, Elongated square bipyramid, Face (geometry), First stellation of rhombic dodecahedron, Geometry, Golden ratio, Great dodecahedron, Great stellated dodecahedron, Hendecagon, Hexagon, Hexagonal antiprism, Hexagonal bipyramid, Hexagonal prism, Hexagonal trapezohedron, Honeycomb (geometry), Icosahedral symmetry, Icosahedron, Isohedral figure, Johnson solid, Kepler–Poinsot polyhedron, Kite (geometry), Limiting case (mathematics), Metabidiminished icosahedron, Net (polyhedron), Octahedral symmetry, Pentagon, Pentagonal antiprism, Pentagonal cupola, Pentagram, ..., Pentakis dodecahedron, Platonic solid, Polyhedron, Pyramid (geometry), Pyrite, Quasicrystal, Quasiregular polyhedron, Regular 4-polytope, Regular dodecahedron, Rhombic dodecahedron, Rhombic triacontahedron, Roman dodecahedron, Rotational symmetry, Schläfli symbol, Small stellated dodecahedron, Snub disphenoid, Snub dodecahedron, Stanko Bilinski, Stellation, Tetrahedral symmetry, Trapezo-rhombic dodecahedron, Trapezoid, Triakis tetrahedron, Triangle, Triangular orthobicupola, Truncated dodecahedron, Truncated tetrahedron, Truncated trapezohedron, University of Ljubljana, University of Wisconsin–Green Bay, Vertex (geometry), VRML, Weaire–Phelan structure, Wedge (geometry), Zonohedron, 120-cell. Expand index (36 more) »

Archimedean solid

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

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Bilinski dodecahedron

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

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Cobaltite

Cobaltite is a sulfide mineral composed of cobalt, arsenic, and sulfur, CoAsS.

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Compound of two icosahedra

This uniform polyhedron compound is a composition of 2 icosahedra.

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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 set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

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Conway polyhedron notation

In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations.

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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).

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Crystal habit

In mineralogy, crystal habit is the characteristic external shape of an individual crystal or crystal group.

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Crystallographic point group

In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind.

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Crystallography

Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure).

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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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Cubic crystal system

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.

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Cuboctahedron

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

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Cupola (geometry)

In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles.

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Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

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Decagonal prism

In geometry, the decagonal prism is the eighth in the infinite set of prisms, formed by ten square side faces and two regular decagon caps.

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Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

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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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Elongated dodecahedron

In geometry, the elongated dodecahedron, extended rhombic dodecahedron, rhombo-hexagonal dodecahedron or hexarhombic dodecahedron is a convex dodecahedron with 8 rhombic and 4 hexagonal faces.

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Elongated square bipyramid

In geometry, the elongated square bipyramid (or elongated octahedron) is one of the Johnson solids (J15).

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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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First stellation of rhombic dodecahedron

In geometry, the first stellation of the rhombic dodecahedron is a stellation of the rhombic dodecahedron.

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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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Great dodecahedron

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.

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Great stellated dodecahedron

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol.

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Hendecagon

In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon.

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Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

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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.

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Hexagonal bipyramid

A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases.

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Hexagonal prism

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

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Hexagonal trapezohedron

The hexagonal trapezohedron or deltohedron is the fourth in an infinite series of face-uniform polyhedra which are dual polyhedron to the antiprisms.

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Honeycomb (geometry)

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.

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Icosahedral symmetry

A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 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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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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Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

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Kite (geometry)

In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

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Limiting case (mathematics)

In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values.

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Metabidiminished icosahedron

In geometry, the metabidiminished icosahedron is one of the Johnson solids (J62).

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Net (polyhedron)

In geometry a net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.

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Octahedral symmetry

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation.

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Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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Pentagonal antiprism

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

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Pentagonal cupola

In geometry, the pentagonal cupola is one of the Johnson solids (J5).

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Pentagram

A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.

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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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Platonic solid

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

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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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Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

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Pyrite

The mineral pyrite, or iron pyrite, also known as fool's gold, is an iron sulfide with the chemical formula FeS2 (iron(II) disulfide).

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Quasicrystal

A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic.

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Quasiregular polyhedron

In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.

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Regular 4-polytope

In mathematics, a regular 4-polytope is a regular four-dimensional polytope.

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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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Rhombic dodecahedron

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

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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.

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Roman dodecahedron

A Roman dodecahedron is a small hollow object made of bronze or stone, with a dodecahedral shape: twelve flat pentagonal faces, each face having a circular hole of varying diameter in the middle, the holes connecting to the hollow center.

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Rotational symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

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Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

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Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.

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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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Snub dodecahedron

In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.

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Stanko Bilinski

Stanko Bilinski (22 April 1909 in Našice – 6 April 1998 in Zagreb) was a Croatian mathematician and academician.

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Stellation

In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.

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Tetrahedral symmetry

A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.

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Trapezo-rhombic dodecahedron

In geometry, the trapezo-rhombic dodecahedron or rhombo-trapezoidal dodecahedron is a convex dodecahedron with 6 rhombic and 6 trapezoidal faces.

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Trapezoid

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English but as a trapezium in English outside North America.

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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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Triangle

A triangle is a polygon with three edges and three vertices.

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Triangular orthobicupola

In geometry, the triangular orthobicupola is one of the Johnson solids (J27).

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Truncated dodecahedron

In geometry, the truncated dodecahedron is an Archimedean solid.

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Truncated tetrahedron

In geometry, the truncated tetrahedron is an Archimedean solid.

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Truncated trapezohedron

An n-gonal truncated trapezohedron is a polyhedron formed by a n-gonal trapezohedron with n-gonal pyramids truncated from its two polar axis vertices.

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University of Ljubljana

The University of Ljubljana (Univerza v Ljubljani, acronym: UL, Universitas Labacensis) is the oldest and largest university in Slovenia.

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University of Wisconsin–Green Bay

The University of Wisconsin–Green Bay (also known as UW–Green Bay or UWGB) is a public university located in Green Bay, Wisconsin, United States.

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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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VRML

VRML (Virtual Reality Modeling Language, pronounced vermal or by its initials, originally—before 1995—known as the Virtual Reality Markup Language) is a standard file format for representing 3-dimensional (3D) interactive vector graphics, designed particularly with the World Wide Web in mind.

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Weaire–Phelan structure

In geometry, the Weaire–Phelan structure is a complex 3-dimensional structure representing an idealised foam of equal-sized bubbles.

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Wedge (geometry)

In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces.

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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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120-cell

In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.

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12-face, 12-hedron, Concave pyritohedral dodecahedron, Dodecahedra, Dodecahedral, Dodekahedron, Doe (geometry), Endo-dodecahedron, Hyperpentagon, Pentadodecahedron, Pyritohedra, Pyritohedron, Small stellatriakis icosahedron, Tetaroid, Tetartoid, Tetartoid (crystallography).

References

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

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