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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)} $

See Also

Space Antiderivatives
Vertex count · Edge length · Surface area · Surcell volume · Surteron bulk · Surpeton pentavolume · Surecton hexavolume · Surzetton heptavolume · Suryotton octavolume
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