Connecting opposite vertices with his pen, Langdon's fingers were trembling.

Six of these are the equatorial decagons to a pair of opposite vertices.

This time we rotate about the axis passing through two opposite vertices (the endpoints of a main diagonal).

What then is the resistance that would be measured between two opposite vertices?

Crease along the three diameters between opposite vertices.

In this notation the mirrors are labeled by the reflection-order of the opposite vertex.

The maximum in 3 dimensions is 6: we can take lines through opposite vertices of an icosahedron.

The four patches and four separating curves all meet at two opposite vertices.

Truncation of two opposite vertices results in a square bifrustum.

For example, the altitude of a triangle is the distance from its base to the opposite vertex.