Vertex count

The vertex count of a shape is the total number of vertices in the shape. It can be considered to be the total extent of all the shape's 0-subfacets in 0-dimensional space. Extruding a shape into a prism doubles the vertex count. Joining a shape into a pyramid increases the vertex count by 1.

Vertex count is unitless.

A vertex is a point where n + |x| multiple faces meet in n dimensions.

Vertex Count Formulae

0-Dimensional

Shape	Count Formula
Point	$1$

1-Dimensional

Shape	Count Formula
Line segment	$2$

2-Dimensional

Shape	Count Formula
Square	$4$
Regular P-gon	$p$

3-Dimensional

Shape	Count Formula
Tetrahedron	$4$
Cube	$8$
Octahedron	$6$
Dodecahedron	$20$
Icosahedron	$12$
Regular P,Q-hedron	$\frac{4p}{4-\left(p-2\right)\left(q-2\right)}$