Namespaces
Variants
Actions

Difference between revisions of "User:Richard Pinch/sandbox-11"

From Encyclopedia of Mathematics
Jump to: navigation, search
m (→‎Honeycomb: link)
(Start article: Glide)
Line 23: Line 23:
 
====References====
 
====References====
 
* H.S.M. Coxeter,  "Regular complex polytopes" , Cambridge Univ. Press  (1974) ISBN 0-521-20125-X  {{ZBL|0732.51002}}
 
* H.S.M. Coxeter,  "Regular complex polytopes" , Cambridge Univ. Press  (1974) ISBN 0-521-20125-X  {{ZBL|0732.51002}}
 +
 +
=Glide=
 +
''glide reflection''
 +
 +
An isometry of the Euclidean plane.  Given a line $\ell$, the glide with axis $\ell$ is a composite of a translation in the direction of $\ell$ and [[reflection]] in $\ell$ as mirror. 
 +
 +
====References====
 +
H. S. M. Coxeter, "The Beauty of Geometry: Twelve Essays" Dover (1999) ISBN 0486409198  {{ZBL|0941.51001}}

Revision as of 07:40, 17 December 2017

Honeycomb

"A symmetrical subdivision of a three-dimensional manifold into a number of polyhedral cells all alike, each rotation that is a symmetry of a cell being also a symmetry of the entire configuration."

A regular honeycomb is described by a Schläfli symbol $\{p,q,r\}$ denoting polyhedral cells that are Platonic solids $\{p,q\}$, such that every face $\{p\}$ belongs to just two cells, and every edge to $r$ cells.

References

  • H.S.M. Coxeter "Twisted honeycombs", Conference Board of the Mathematical Sciences. Regional Conference Series in Mathematics. No.4. American Mathematical Society (1970) ISBN 0-8218-1653-5 Zbl 0217.46502
  • H.S.M. Coxeter, "Regular complex polytopes" , Cambridge Univ. Press (1974) ISBN 0-521-20125-X Zbl 0732.51002

Schläfli symbol

A symbol encoding classes of polygons, polyhedra, polytopes and tessellations.

The symbol $\{p\}$ denotes a regular $p$-gon; the symbol $\{p,q\}$ a polyhedron with faces which are regular $p$-gons, $q$ of which meet at each vertex. The Platonic solids correspond to:

There are three plane tessellations: $\{3,6\}$, $\{4,4\}$, $\{6,3\}$. The dual solid or tessellation to $\{p,q\}$ is $\{q,p\}$.

The symbol $\{p,q,r\}$ denotes a polytope in four dimensions or a honeycomb.

References

  • H.S.M. Coxeter, "Regular complex polytopes" , Cambridge Univ. Press (1974) ISBN 0-521-20125-X Zbl 0732.51002

Glide

glide reflection

An isometry of the Euclidean plane. Given a line $\ell$, the glide with axis $\ell$ is a composite of a translation in the direction of $\ell$ and reflection in $\ell$ as mirror.

References

H. S. M. Coxeter, "The Beauty of Geometry: Twelve Essays" Dover (1999) ISBN 0486409198 Zbl 0941.51001

How to Cite This Entry:
Richard Pinch/sandbox-11. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Richard_Pinch/sandbox-11&oldid=42538