(Will be extended from time to time.)

##### connected

a net is connected, if there is a continous path from every vertex to every other vertex

##### embedding

a graph/net, in which the vertices have been assigned (eucledian) coordinates; this implies that now the edges have a certain length

##### graph

an abstract mathematical object in which *vertices* are connected by *edges*

*k*-connected

an *k*-connected graph is a graph in which *k* numbers of vertices (and their edges) have to be deleted to separate the graph into two parts

graphs, which consists of vertices which are all 3-coordinated can be indeed only 2-connected:

if the two orange vertices were deleted, the graph is *disjoint*

*n*-coordinated

an *n*-coordinated vertex has *n* connections to other vertices, *n* is the coordination number

shortform: n-c, for instance **nbo** is a 4-c net

if two or more vertices with different coordination numbers are present, the different *coordination numbers* of the vertices are separated by commas and are enclosed in brackets, for instance the net **tbo** is a (3,4)-c net

sometimes, a multinodal net is specified only in its short or compact form, i.e. only the different coordination numbers are given, in other cases every non-symmetry-related vertex is explicitely specified with its coordination number, for instance **zhc** is a octanodal (3,3,3,3,4,4,4,4)-c net; its short notation is again only (3,4)-c;

##### net

a finite or periodic, connected, and simple *graph*

simple means that the edges have *no directions* and that it contains no *loops (*edges linking a vertex to itself), and that there are *no multiple edges* between any vertices

##### quasiregular net

a quasiregular net is characterized by the transitivity *pqrs* = 1112

there is only one quasiregular net:

**fcu**

##### regular net

a regular net is characterized by the transitivity *pqrs* = 1111

there are only 5 regular nets:

**bcu**, **dia**, **nbo**, **pcu**, and **srs**

a regular net is *vertex*– as well as *edge-transitive*

**semiregular net**

a semiregular net is characterized by the transitivity *pqrs* = 11*rs* (with *r* > 1)

there are 16 semiregular nets:

**lvt**, **sod**, **lcs**, **lcv**, **qtz**, **hxg**, **lcy**, **crs**, **bcs**, **acs**, **reo**, **thp**, **rhr**, **ana, ibb, and icc**

a semiregular net is *vertex*– as well as *edge-transitive*

Stephen hydeCan you include a definition of a “net”? I recall some discussion about this.

doktorholzPost authoryes, will expand the glossary right after my holiday!

Stephen hydeI was curious to remind myself of the definition… Happy holiday.