This is an indexed list of the uniform and stellated polyhedra from the book ''Polyhedron Models'', by
Magnus Wenninger
Father Magnus J. Wenninger Order of Saint Benedict, 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.
Early life ...
.
The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes. It contains the 75 nonprismatic
uniform polyhedra
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent.
Uniform polyhedra may be regular (if also fa ...
, as well as 44
stellated forms of the convex regular and quasiregular polyhedra.
Models listed here can be cited as "Wenninger Model Number ''N''", or ''W''
''N'' for brevity.
The polyhedra are grouped in 5 tables: Regular (1–5), Semiregular (6–18), regular star polyhedra (20–22,41), Stellations and compounds (19–66), and uniform star polyhedra (67–119). ''The four regular star polyhedra are listed twice because they belong to both the uniform polyhedra and stellation groupings.''
Platonic solids
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...
(regular convex polyhedra) W1 to W5
Archimedean solids
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed o ...
(Semiregular) W6 to W18
Kepler–Poinsot polyhedra (Regular
star polyhedra
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.
There are two general kinds of star polyhedron:
*Polyhedra which self-intersect in a repetitive way.
*Concave p ...
) W20, W21, W22 and W41
Stellations: models W19 to W66
Stellations of octahedron
Stellations of dodecahedron
Stellations of icosahedron
Stellations of cuboctahedron
Stellations of icosidodecahedron
Uniform nonconvex solids W67 to W119
See also
*
List of uniform polyhedra
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive ( transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are c ...
*
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. It enumerates certain stellations of the regular convex or Platonic icosahedron, according to a set of rules put for ...
*
List of polyhedral stellations
References
*
** Errata
*** In Wenninger, the vertex figure for W90 is incorrectly shown as having parallel edges.
*
External links
Magnus J. Wenninger* Software used to generate images in this article:
*
Stella: Polyhedron NavigatorStella (software)
Stella, a computer program available in three versions (Great Stella, Small Stella and Stella4D), was created by Robert Webb of Australia. The programs contain a large library of polyhedra which can be manipulated and altered in various ways.
...
- Can create and print nets for all of Wenninger's polyhedron models.
*
Vladimir Bulatov's Polyhedra Stellations Applet*
Vladimir Bulatov's Polyhedra Stellations Applet packaged as an OS X application known errors in the various editions.
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Polyhedra
Polyhedral stellation
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