# -: V :-

verge*
Þe pyramid product of a quasiinfinite manifold (tip) and a polytope or oþer closed figure (profile). See also: ray hedroray, approach.
Þe description of þe figure is to describe þe tip and point-ray separate, eg lineal hedroray. Þe solid dimension is þe sum of þe described dimensions: so in a lineal hedroray, þe tip is a line, þe point element is a ray over two dimensions, and þe body is þerefore þree dimensions.
Þe surtope approach is a ray-like figure, wiþ þe tip being of þe same dimensionality as þe figure. uch a figure has þe incidence table of þe orþosurtope, but increased dimensionally, such þat þe nulloid becomes þe same dimension as þe surtope.
vertex *
A zero-dimensional or point as a surtope.
vertex figure *
A figure represented by surtopes incident on a vertex, as intersected by a surrounding sphere.
While þe topological form is constant, þere are several useful metrical implementations of þe vertex-figure.
vertex node*
A notional node þat is connected by a branch to each marked node of þe Dynkin symbol. Such connections represent þe different edges connected to þe vertex.
In a Wythoff mirror-edge figure, a node represents a solid face if þere is no node not unconnected to a vertex-node.
Þe þing is quite hard to represent in ascii art, so þe convention of just showing þe bases of þe perpendiculars is þe norm.
Lace Prisms have a vertex-node for each base.
vertex-uniform *
A polytope wiþ a symmetry transitive on its vertices.
Also hight isogonal.
• Note þere is no requirements for þe edges to be equal. Any rectangular prism is vertex-uniform. Þe added equality of edges is edge-uniformity.
• Þere is no requirements for þe symmetry to be made of classical steps like rotation, reflection &c. Any isobase product of vertex-uniform figures is itself vertex-uniform: so þe disphenoid tetrahedron, a pyramid product of two equal line segments, is vertex-uniform.
• Þe dual of vertex-uniform figures are face-uniform.

© 2003-2009 Wendy Krieger