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The Fifty-Nine Icosahedra

Index The Fifty-Nine Icosahedra

The Fifty-Nine Icosahedra is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie. [1]

32 relations: A. Harry Wheeler, Cambridge University Press, Chirality (mathematics), Collotype, Combinatorics, Compound of five octahedra, Compound of five tetrahedra, Compound of ten tetrahedra, Echidna, Excavated dodecahedron, Final stellation of the icosahedron, Graph theory, Great icosahedron, Great triambic icosahedron, Harold Scott MacDonald Coxeter, Icosahedron, International Congress of Mathematicians, J. C. P. Miller, Johannes Kepler, Kepler–Poinsot polyhedron, Magnus Wenninger, Max Brückner, Patrick du Val, Platonic solid, Polytope compound, Reflection (mathematics), Regular icosahedron, Small triambic icosahedron, Solids with icosahedral symmetry, Stellation, Stellation diagram, University of Toronto.

A. Harry Wheeler

Albert Harry Wheeler (18 January 1873, Leominster, Massachusetts – 1950) was an American mathematician, inventor, and mathematics teacher, known for physical construction (usually in paper) of polyhedral models and teaching this art to students.

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Cambridge University Press

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

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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.

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Collotype

Collotype is a dichromate-based photographic process invented by Alphonse Poitevin in 1856, and used for large-volume mechanical printing before the introduction of cheaper offset lithography.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

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Compound of five octahedra

The compound of five octahedra is one of the five regular polyhedron compounds.

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Compound of five tetrahedra

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

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Compound of ten tetrahedra

The compound of ten tetrahedra is one of the five regular polyhedral compounds.

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Echidna

Echidnas, sometimes known as spiny anteaters, belong to the family Tachyglossidae in the monotreme order of egg-laying mammals.

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Excavated dodecahedron

In geometry, the excavated dodecahedron is a star polyhedron having 60 equilateral triangular faces.

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Final stellation of the icosahedron

In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram.

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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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.

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Great triambic icosahedron

In geometry, the great triambic icosahedron and medial triambic icosahedron are visually identical dual uniform polyhedra.

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Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

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Icosahedron

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

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International Congress of Mathematicians

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics.

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J. C. P. Miller

Jeffrey Charles Percy Miller (31 August 1906 – 24 April 1981) was an English mathematician and computing pioneer.

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Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

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Kepler–Poinsot polyhedron

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

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Magnus Wenninger

Father Magnus J. Wenninger OSB (October 31, 1919Banchoff (2002)– February 17, 2017) was an American mathematician who worked on constructing polyhedron models, and wrote the first book on their construction.

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Max Brückner

Johannes Max Brückner (5 August 1860 – 1 November 1934) was a German geometer, known for his collection of polyhedral models.

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Patrick du Val

Patrick du Val (March 26, 1903 – January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity.

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Platonic solid

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

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Polytope compound

A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.

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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 icosahedron

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

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Small triambic icosahedron

In geometry, the small triambic icosahedron is the dual to the uniform small ditrigonal icosidodecahedron.

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Solids with icosahedral symmetry

Platonic solids - regular polyhedra (all faces of the same type) Archimedean solids - polyhedra with more than one polygon face type.

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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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Stellation diagram

In geometry, a stellation diagram or stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other face planes intersect with this one.

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University of Toronto

The University of Toronto (U of T, UToronto, or Toronto) is a public research university in Toronto, Ontario, Canada on the grounds that surround Queen's Park.

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References

[1] https://en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra

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