(Will be extended from time to time.)


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


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


an abstract mathematical object in which vertices are connected by edges


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


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;


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:

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 = 11rs (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

uniform net

in a uniform net at all angles the shortest rings are all of the same size


3 thoughts on “Glossary

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