  This paper presents an additional class of regular polyhedra--envelope
polyhedra--made of regular polygons, where the arrangement of polygons
(creating a single surface) around each vertex is identical; but dihedral
angles between faces need not be identical, and some of the dihedral angles are
0 degrees (i.e., some polygons are placed back to back). For example, squares,
6 around a point, is produced by deleting the triangles from the
rhombicuboctahedron, creating a hollow polyhedron of genus 7 with triangular
holes connecting 18 interior and 18 exterior square faces. An empty cube
missing its top and bottom faces becomes an envelope polyhedron, squares, 4
around a point, with a toroidal topology. This definition leads to many
interesting finite and infinite multiply connected regular polygon networks,
including one infinite network with squares, 14 around a point, and another
with triangles, 18 around a point. These are introduced just over 50 years
after my related paper on infinite spongelike pseudopolyhedra in American
Mathematical Monthly (Gott, 1967).
