Tetrakis hexahedron, the Glossary

Table of Contents

1. 56 relations: Archimedean solid, Barycentric subdivision, Building (mathematics), Cambridge University Press, Cartesian coordinate system, Catalan solid, Compound of three octahedra, Conway polyhedron notation, Copper, Crystal, Crystal model, Cube, Cubic pyramid, Deltoidal icositetrahedron, Dice, Disdyakis dodecahedron, Disdyakis triacontahedron, Divina proportione, Dual polyhedron, Equilateral triangle, Fluorite, Gamer, Geometry, Great circle, Group (mathematics), Hosohedron, Kleetope, Leonardo da Vinci, Luca Pacioli, Net (polyhedron), Octahedron, Omnitruncation, Orthographic projection, Perspectiva corporum regularium, Perspective (graphical), Polytope compound, Pythagorean theorem, Reflection (mathematics), Rhombic dodecahedron, Simplex, Special linear group, Spherical polyhedron, Square pyramid, Stereographic projection, Symmetric space, Symmetry group, Tetrahedral symmetry, Tetrahedron, Tits metric, Triakis tetrahedron, ... Expand index (6 more) »

2. Catalan solids

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 Tetrakis hexahedron and Archimedean solid

Barycentric subdivision

In mathematics, the barycentric subdivision is a standard way to subdivide a given simplex into smaller ones.

See Tetrakis hexahedron and Barycentric subdivision

Building (mathematics)

In mathematics, a building (also Tits building, named after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces.

See Tetrakis hexahedron and Building (mathematics)

Cambridge University Press

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

See Tetrakis hexahedron and Cambridge University Press

Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

See Tetrakis hexahedron and Cartesian coordinate system

Catalan solid

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

See Tetrakis hexahedron and Catalan solid

Compound of three octahedra

In mathematics, the compound of three octahedra or octahedron 3-compound is a polyhedral compound formed from three regular octahedra, all sharing a common center but rotated with respect to each other.

See Tetrakis hexahedron and Compound of three octahedra

Conway polyhedron notation

In geometry and topology, 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.

See Tetrakis hexahedron and Conway polyhedron notation

Copper

Copper is a chemical element; it has symbol Cu and atomic number 29.

See Tetrakis hexahedron and Copper

Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

See Tetrakis hexahedron and Crystal

Crystal model

A crystal model is a teaching aid used for understanding concepts in crystallography and the morphology of crystals.

See Tetrakis hexahedron and Crystal model

Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces.

See Tetrakis hexahedron and Cube

Cubic pyramid

In 4-dimensional geometry, the cubic pyramid is bounded by one cube on the base and 6 square pyramid cells which meet at the apex.

See Tetrakis hexahedron and Cubic pyramid

Deltoidal icositetrahedron

In geometry, the deltoidal icositetrahedron (or trapezoidal icositetrahedron, tetragonal icosikaitetrahedron, tetragonal trisoctahedron, strombic icositetrahedron) is a Catalan solid. Tetrakis hexahedron and deltoidal icositetrahedron are Catalan solids.

See Tetrakis hexahedron and Deltoidal icositetrahedron

Dice

Dice (die or dice) are small, throwable objects with marked sides that can rest in multiple positions.

See Tetrakis hexahedron and Dice

Disdyakis dodecahedron

In geometry, a disdyakis dodecahedron, (also hexoctahedron, hexakis octahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron), is a Catalan solid with 48 faces and the dual to the Archimedean truncated cuboctahedron. Tetrakis hexahedron and disdyakis dodecahedron are Catalan solids.

See Tetrakis hexahedron and Disdyakis dodecahedron

Disdyakis triacontahedron

In geometry, a disdyakis triacontahedron, hexakis icosahedron, decakis dodecahedron or kisrhombic triacontahedron is a Catalan solid with 120 faces and the dual to the Archimedean truncated icosidodecahedron. Tetrakis hexahedron and disdyakis triacontahedron are Catalan solids.

See Tetrakis hexahedron and Disdyakis triacontahedron

Divina proportione

Divina proportione (15th century Italian for Divine proportion), later also called De divina proportione (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, completed by February 9th, 1498 in Milan and first printed in 1509.

See Tetrakis hexahedron and Divina proportione

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 Tetrakis hexahedron and Dual polyhedron

Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides have the same length.

See Tetrakis hexahedron and Equilateral triangle

Fluorite

Fluorite (also called fluorspar) is the mineral form of calcium fluoride, CaF2.

See Tetrakis hexahedron and Fluorite

Gamer

A gamer is a someone who plays interactive games, either video games, tabletop role-playing games, skill-based card games, or any combination thereof, and who often plays for extended periods of time.

See Tetrakis hexahedron and Gamer

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Tetrakis hexahedron and Geometry

Great circle

In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.

See Tetrakis hexahedron and Great circle

Group (mathematics)

In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.

See Tetrakis hexahedron and Group (mathematics)

Hosohedron

In spherical geometry, an n-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.

See Tetrakis hexahedron and Hosohedron

Kleetope

In geometry and polyhedral combinatorics, the Kleetope of a polyhedron or higher-dimensional convex polytope is another polyhedron or polytope formed by replacing each facet of with a pyramid.

See Tetrakis hexahedron and Kleetope

Leonardo da Vinci

Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.

See Tetrakis hexahedron and Leonardo da Vinci

Luca Pacioli

Luca Bartolomeo de Pacioli, O.F.M. (sometimes Paccioli or Paciolo; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting.

See Tetrakis hexahedron and Luca Pacioli

Net (polyhedron)

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

See Tetrakis hexahedron and Net (polyhedron)

Octahedron

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

See Tetrakis hexahedron and Octahedron

Omnitruncation

In geometry, an omnitruncation of a convex polytope is a simple polytope of the same dimension, having a vertex for each flag of the original polytope and a facet for each face of any dimension of the original polytope.

See Tetrakis hexahedron and Omnitruncation

Orthographic projection

Orthographic projection (also orthogonal projection and analemma) is a means of representing three-dimensional objects in two dimensions.

See Tetrakis hexahedron and Orthographic projection

Perspectiva corporum regularium

Perspectiva corporum regularium (from Latin: Perspective of the Regular Solids) is a book of perspective drawings of polyhedra by German Renaissance goldsmith Wenzel Jamnitzer, with engravings by Jost Amman, published in 1568.

See Tetrakis hexahedron and Perspectiva corporum regularium

Perspective (graphical)

Linear or point-projection perspective is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection.

See Tetrakis hexahedron and Perspective (graphical)

Polytope compound

In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.

See Tetrakis hexahedron and Polytope compound

Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

See Tetrakis hexahedron and Pythagorean theorem

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 Tetrakis hexahedron and Reflection (mathematics)

Rhombic dodecahedron

In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. Tetrakis hexahedron and rhombic dodecahedron are Catalan solids.

See Tetrakis hexahedron and Rhombic dodecahedron

Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

See Tetrakis hexahedron and Simplex

Special linear group

In mathematics, the special linear group of degree n over a commutative ring R is the set of matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion.

See Tetrakis hexahedron and Special linear group

Spherical polyhedron

In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.

See Tetrakis hexahedron and Spherical polyhedron

Square pyramid

In geometry, a square pyramid is a pyramid with a square base, having a total of five faces.

See Tetrakis hexahedron and Square pyramid

Stereographic projection

In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point.

See Tetrakis hexahedron and Stereographic projection

Symmetric space

In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of isometries contains an inversion symmetry about every point.

See Tetrakis hexahedron and Symmetric space

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 Tetrakis hexahedron and Symmetry group

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.

See Tetrakis hexahedron and Tetrahedral symmetry

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 Tetrakis hexahedron and Tetrahedron

Tits metric

In mathematics, the Tits metric is a metric defined on the ideal boundary of an Hadamard space (also called a complete CAT(0) space).

See Tetrakis hexahedron and Tits metric

Triakis tetrahedron

In geometry, a triakis tetrahedron (or kistetrahedron) is a Catalan solid with 12 faces. Tetrakis hexahedron and triakis tetrahedron are Catalan solids.

See Tetrakis hexahedron and Triakis tetrahedron

Triangle

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.

See Tetrakis hexahedron and Triangle

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.

See Tetrakis hexahedron and Truncated octahedron

Truncated trihexagonal tiling

In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane.

See Tetrakis hexahedron and Truncated trihexagonal tiling

Vertex configuration

In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.

See Tetrakis hexahedron and Vertex configuration

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.

See Tetrakis hexahedron and VRML

Wenzel Jamnitzer

Wenzel Jamnitzer (sometimes Jamitzer, or Wenzel Gemniczer) (1507/1508 – 19 December 1585) was a Northern Mannerist goldsmith, artist, and printmaker in etching, who worked in Nuremberg.

See Tetrakis hexahedron and Wenzel Jamnitzer

See also

Catalan solids

• Catalan solid
• Deltoidal hexecontahedron
• Deltoidal icositetrahedron
• Disdyakis dodecahedron
• Disdyakis triacontahedron
• Pentagonal hexecontahedron
• Pentagonal icositetrahedron
• Pentakis dodecahedron
• Rhombic dodecahedron
• Rhombic triacontahedron
• Tetrakis hexahedron
• Triakis icosahedron
• Triakis octahedron
• Triakis tetrahedron

References

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

Also known as Disdyakis cube, Disdyakis hexahedron, Disdyakishexahedron, Hexakis tetrahedron, Hextetrahedron, Kiscube, Tetrahexahedron, Tetrakis cube, Tetrakis hexahedra, Tetrakishexahedron.

, Triangle, Truncated octahedron, Truncated trihexagonal tiling, Vertex configuration, VRML, Wenzel Jamnitzer.