𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Completely classifying all vertex-transitive and edge-transitive polyhedra

✍ Scribed by Steven L. Farris

Book ID
104642072
Publisher
Springer
Year
1988
Tongue
English
Weight
495 KB
Volume
26
Category
Article
ISSN
0046-5755

No coin nor oath required. For personal study only.

✦ Synopsis

Recently A. Dress completed the classification of the regular polyhedra in E 3 by adding one class to the enumeration given by Gr/inbaum on this subject. This classification is the only systematic study of a collection of polyhedra possessing special symmetries which uses the generalized definition of a polygon allowing for skew polygons as well as planar polygons in E 3. This study gives necessary conditions for polyhedra to be vertex-transitive and.edgetransitive. These conditions are restrictive enough to make the task of completely enumerating such polyhedra realizable and efficient. Examples of this process are given, and an explanation of the basic process is discussed. These 'new' polyhedra are appearing more frequently in applications of geometry, and this examination is a beginning of the classifications of polyhedra having special symmetries even though there are many other such classes which lack this scrutiny.

📜 SIMILAR VOLUMES

The edge-transitive but not vertex-trans
The edge-transitive but not vertex-transitive cubic graph on 112 vertices
✍ Marston Conder; Aleksander Malnič; Dragan Marušič; Tomaž Pisanski; Primož Potočn 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 220 KB 👁 1 views

## Abstract A detailed description is given of a recently discovered edge‐transitive but not vertex‐transitive trivalent graph on 112 vertices, which turns out to be the third smallest example of such a semisymmetric cubic graph. This graph has been called the __Ljubljana graph__ by the first autho

On the Edge Connectivity, Hamiltonicity,
On the Edge Connectivity, Hamiltonicity, and Toughness of Vertex-Transitive Graphs
✍ Jan van den Heuvel; Bill Jackson 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 191 KB

Let G be a connected k-regular vertex-transitive graph on n vertices. For S V(G) let d(S) denote the number of edges between S and V(G)"S. We extend results of Mader and Tindell by showing that if d(S)< 2 9 (k+1) 2 for some S V(G) with 1 3 (k+1) |S| 1 2 n, then G has a factor F such that GÂE(F ) is

An infinite series of regular edge- but
An infinite series of regular edge- but not vertex-transitive graphs
✍ Felix Lazebnik; Raymond Viglione 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 91 KB 👁 1 views

## Abstract Let __n__ be an integer and __q__ be a prime power. Then for any 3 ≤ __n__ ≤ __q__−1, or __n__=2 and __q__ odd, we construct a connected __q__‐regular edge‐but not vertex‐transitive graph of order 2__q__^__n__+1^. This graph is defined via a system of equations over the finite field of