# Regular and semi-regular polytopes. II

@article{Coxeter1940RegularAS, title={Regular and semi-regular polytopes. II}, author={H. S. M. Coxeter}, journal={Mathematische Zeitschrift}, year={1940}, volume={188}, pages={559-591} }

Groupes de reflexion a 4 dimensions. Certains sous groupes d'indice petit. Construction de Wythoff et ses consequences numeriques. Polytopes a 4 dimensions. Nids d'abeilles a 4 dimensions. L'analogue a 4 dimensions du cube de Snub. Le grand antiprisme

## 77 Citations

### On the Size of Equifacetted Semi-Regular Polytopes

- Mathematics
- 2011

Unlike the situation in the classical theory of convex polytopes, there is a wealth of semi-regular abstract polytopes, including interesting examples exhibiting some unexpected phenomena. We prove…

### Spectra of semi-regular polytopesNicolau

- Mathematics
- 2007

We compute the spectra of the adjacency matrices of the semi-regular polytopes. A few diierent techniques are employed: the most sophisticated, which relates the 1-skeleton of the polytope to a…

### Polytopes with Preassigned Automorphism Groups

- MathematicsDiscret. Comput. Geom.
- 2015

We prove that every finite group is the automorphism group of a finite abstract polytope isomorphic to a face-to-face tessellation of a sphere by topological copies of convex polytopes. We also show…

### Some examples of semi-nodal perfect 4-polytopes

- MathematicsPublicationes Mathematicae Debrecen
- 2003

Existence of a semi-nodal perfect polytope means that there is a perfect polytope P such that both P and its polar P ∗ has vertices of not only zero degree of freedom. Yet, it is perfect, i.e. its…

### Polytopes, quasi-minuscule representations and rational surfaces

- Mathematics
- 2017

We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we…

### Regular and chiral polytopes in low dimensions

- Mathematics
- 2005

There are two main thrusts in the theory of regular and chi- ral polytopes: the abstract, purely combinatorial aspect, and the geo- metric one of realizations. This brief survey concentrates on the…

### A Hierarchical Classification of Euclidean Polytopes with Regularity Properties

- Mathematics
- 1994

During the last decades, many mathematicians investigated classes of poly topes which are determined by natural weakenings of the definitions of regular polytopes. Examples are the sets of…

### On Perfect 4-Polytopes

- Mathematics
- 2002

The concept of perfection of a polytope was introduced by S. A. Robertson. Intuitively speaking, a polytope P is perfect if and only if it cannot be deformed to a polytope of dierent shape without…

## References

SHOWING 1-10 OF 17 REFERENCES

### Finite groups generated by reflections, and their subgroups generated by reflections

- Mathematics
- 1934

In connection with his work on singularities of surfaces, Du Val asked me to enumerate certain subgroups in the symmetry groups of the “pure Archimedean” polytopes n21 (n < 5), namely those subgroups…

### The Pure Archimedean Polytopes in Six and Seven Dimensions

- Mathematics
- 1928

An Archimedean solid (in three dimensions) may be defined as a polyhedron whose faces are regular polygons of two or more kinds and whose vertices are all surrounded in the same way. For example, the…

### Mathematical Recreations and Essays

- MathematicsNature
- 1905

THIS edition differs from the third by containing chapters on the history of the mathematical tripos at Cambridge, Mersenne's numbers, and cryptography and ciphers, besides descriptions of some…

### The Polytope 2 21 Whose Twenty-Seven Vertices Correspond to the Lines to the General Cubic Surface

- Mathematics
- 1940