1. On the Facets and Corners of Flat-Faced Solids

Extract

In this paper it was shown that the usually received theorems concerning the faces of polyhedrons are true only of one class of solids. The theorem that “no solid can have every one of its faces more than pentagonal” was contradicted by the exhibitionof a solid bounded entirely by hexagons. Each corner of this solid is trihedral, and the sum of all its angles amounts to four times as many right angles as there are corners; whereas the usual theorem is, that “the angles of any solid amount to four times as many right angles as there are corners, lesseight.”