Wider Scope: List of Polyhedra by Type

Truncated polyhedra are regular polyhedra in which the vertices have been cut and replaced with additional faces.

As the cut becomes deeper, the areas of the new faces become greater and further into the shape and the areas of the remaining faces become smaller. If the "cut" is "deep" enough, the new faces can come out of the other side of the shape, creating quasitruncated shapes.

Convex

Truncated Cube

Convex truncated polyhedra are easy to understand, since they are just the platonic solids with the vertices cut off.

Concave

Concave truncated polyhedra are truncated polyhedra that intersect themselves.

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