Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Download
Faster access than browser!
 

Polyhedron and Regular icosahedron

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Polyhedron and Regular icosahedron

Polyhedron vs. Regular icosahedron

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

Similarities between Polyhedron and Regular icosahedron

Polyhedron and Regular icosahedron have 44 things in common (in Unionpedia): American Mathematical Monthly, Angular defect, Antiprism, Chirality (mathematics), Conway polyhedron notation, Digon, Dihedral angle, Dodecahedron, Dual polyhedron, Euclidean space, Face (geometry), Faceting, Geometry, Graph (discrete mathematics), Great dodecahedron, Great icosahedron, Icosahedral symmetry, Icosahedron, Isogonal figure, Johnson solid, K-vertex-connected graph, Kepler–Poinsot polyhedron, N-skeleton, Net (polyhedron), Octahedron, Pappus of Alexandria, Planar graph, Platonic solid, Polytope, Regular polyhedron, ..., Rhombic triacontahedron, Rotation, Skew apeirohedron, Small stellated dodecahedron, Snub cube, Snub dodecahedron, Stellation, Symmetric graph, Symmetry group, Tetrahedral symmetry, Tetrahedron, Vertex figure, Volume, 4-polytope. Expand index (14 more) »

American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

American Mathematical Monthly and Polyhedron · American Mathematical Monthly and Regular icosahedron · See more »

Angular defect

In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the Euclidean plane would.

Angular defect and Polyhedron · Angular defect and Regular icosahedron · See more »

Antiprism

In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.

Antiprism and Polyhedron · Antiprism and Regular icosahedron · See more »

Chirality (mathematics)

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone.

Chirality (mathematics) and Polyhedron · Chirality (mathematics) and Regular icosahedron · See more »

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.

Conway polyhedron notation and Polyhedron · Conway polyhedron notation and Regular icosahedron · See more »

Digon

In geometry, a digon is a polygon with two sides (edges) and two vertices.

Digon and Polyhedron · Digon and Regular icosahedron · See more »

Dihedral angle

A dihedral angle is the angle between two intersecting planes.

Dihedral angle and Polyhedron · Dihedral angle and Regular icosahedron · See more »

Dodecahedron

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

Dodecahedron and Polyhedron · Dodecahedron and Regular icosahedron · See more »

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.

Dual polyhedron and Polyhedron · Dual polyhedron and Regular icosahedron · See more »

Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

Euclidean space and Polyhedron · Euclidean space and Regular icosahedron · See more »

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.

Face (geometry) and Polyhedron · Face (geometry) and Regular icosahedron · See more »

Faceting

Stella octangula as a faceting of the cube In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.

Faceting and Polyhedron · Faceting and Regular icosahedron · See more »

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.

Geometry and Polyhedron · Geometry and Regular icosahedron · See more »

Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

Graph (discrete mathematics) and Polyhedron · Graph (discrete mathematics) and Regular icosahedron · See more »

Great dodecahedron

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

Great dodecahedron and Polyhedron · Great dodecahedron and Regular icosahedron · See more »

Great icosahedron

In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.

Great icosahedron and Polyhedron · Great icosahedron and Regular icosahedron · See more »

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.

Icosahedral symmetry and Polyhedron · Icosahedral symmetry and Regular icosahedron · See more »

Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

Icosahedron and Polyhedron · Icosahedron and Regular icosahedron · See more »

Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

Isogonal figure and Polyhedron · Isogonal figure and Regular icosahedron · See more »

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.

Johnson solid and Polyhedron · Johnson solid and Regular icosahedron · See more »

K-vertex-connected graph

In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.

K-vertex-connected graph and Polyhedron · K-vertex-connected graph and Regular icosahedron · See more »

Kepler–Poinsot polyhedron

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

Kepler–Poinsot polyhedron and Polyhedron · Kepler–Poinsot polyhedron and Regular icosahedron · See more »

N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

N-skeleton and Polyhedron · N-skeleton and Regular icosahedron · See more »

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.

Net (polyhedron) and Polyhedron · Net (polyhedron) and Regular icosahedron · See more »

Octahedron

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

Octahedron and Polyhedron · Octahedron and Regular icosahedron · See more »

Pappus of Alexandria

Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c. 350 AD) was one of the last great Greek mathematicians of Antiquity, known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry.

Pappus of Alexandria and Polyhedron · Pappus of Alexandria and Regular icosahedron · See more »

Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

Planar graph and Polyhedron · Planar graph and Regular icosahedron · See more »

Platonic solid

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

Platonic solid and Polyhedron · Platonic solid and Regular icosahedron · See more »

Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

Polyhedron and Polytope · Polytope and Regular icosahedron · See more »

Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

Polyhedron and Regular polyhedron · Regular icosahedron and Regular polyhedron · See more »

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.

Polyhedron and Rhombic triacontahedron · Regular icosahedron and Rhombic triacontahedron · See more »

Rotation

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

Polyhedron and Rotation · Regular icosahedron and Rotation · See more »

Skew apeirohedron

In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend indefinitely without folding round to form a closed surface.

Polyhedron and Skew apeirohedron · Regular icosahedron and Skew apeirohedron · See more »

Small stellated dodecahedron

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

Polyhedron and Small stellated dodecahedron · Regular icosahedron and Small stellated dodecahedron · See more »

Snub cube

In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles.

Polyhedron and Snub cube · Regular icosahedron and Snub cube · See more »

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.

Polyhedron and Snub dodecahedron · Regular icosahedron and Snub dodecahedron · See more »

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.

Polyhedron and Stellation · Regular icosahedron and Stellation · See more »

Symmetric graph

In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphism such that In other words, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of adjacent vertices (that is, upon edges considered as having a direction).

Polyhedron and Symmetric graph · Regular icosahedron and Symmetric graph · See more »

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.

Polyhedron and Symmetry group · Regular icosahedron and Symmetry group · See more »

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.

Polyhedron and Tetrahedral symmetry · Regular icosahedron and Tetrahedral symmetry · See more »

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.

Polyhedron and Tetrahedron · Regular icosahedron and Tetrahedron · See more »

Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

Polyhedron and Vertex figure · Regular icosahedron and Vertex figure · See more »

Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

Polyhedron and Volume · Regular icosahedron and Volume · See more »

4-polytope

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.

4-polytope and Polyhedron · 4-polytope and Regular icosahedron · See more »

The list above answers the following questions

Polyhedron and Regular icosahedron Comparison

Polyhedron has 210 relations, while Regular icosahedron has 163. As they have in common 44, the Jaccard index is 11.80% = 44 / (210 + 163).

References

This article shows the relationship between Polyhedron and Regular icosahedron. To access each article from which the information was extracted, please visit:

Hey! We are on Facebook now! »