# -: V :-

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