# Convex Polyhedra with Regular Faces

```@article{Johnson1966ConvexPW,
title={Convex Polyhedra with Regular Faces},
author={Norman W. Johnson},
year={1966},
volume={18},
pages={169 - 200}
}```
• N. Johnson
• Published 1966
• Mathematics
An interesting set of geometric figures is composed of the convex polyhedra in Euclidean 3-space whose faces are regular polygons (not necessarily all of the same kind). A polyhedron with regular faces is uniform if it has symmetry operations taking a given vertex into each of the other vertices in turn (5, p. 402). If in addition all the faces are alike, the polyhedron is regular. That there are just five convex regular polyhedra—the so-called Platonic solids—was proved by Euclid in the…
A convex polyhedron with regular faces or with faces decomposable by two regular polygons is called indecomposable if any section plane dissects this polyhedron into two parts so that at least one of
All 3-dimensional convex regular-hedra are found, i.e., the convex polyhedra having positive curvature of each vertex and such that every face is either a regular polygon or is composed of two
BRIDGES Mathematical Connections in Art, Music, and Science An investigation to find polyhedra having faces that include only regular polygons along with a particular concave equilateral pentagon
• Mathematics
Discret. Comput. Geom.
• 2016
The blueprint for the construction is described and the Wythoffians for distinguished classes of regular polyhedra are treated, which are vertex-transitive and often feature vertex configurations with an attractive mix of different face shapes.
For any polyhedron (3-polytope) P in ordinary three-dimensional space let S(P) denote its surface, that is, the union of its (closed) 2-faces. If P 1 and P 2 are given polyhedra, they are said to be
• Mathematics
• 2018
For a finite planar graph, it associates with some metric spaces, called (regular) spherical polyhedral surfaces, by replacing faces with regular spherical polygons in the unit sphere and gluing them
In geometry, any polyhedron with 12 faces is named a dodecahedron, among which only one is the regular dodecahedron (i.e. the Platonic solid), composed of 12 regular pentagonal faces, 3 of which
Depending on the type, considering only the topological structure of the network of faces, and the angles of corresponding faces at corresponding vertices, convex polyhedra in R3, each face of which
Multi-shell clusters represent complex structures, the study of which needs rigorous definitions in graph theory, geometry, set theory, etc. Within this chapter, main definitions for polyhedra,

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### Convex polyhedra with regular faces (preliminary report), Abstract 576-157

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