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**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.

- Note there is no requirements for the

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© 2003-2009 Wendy Krieger