P''

P''
Rank	3
Type	Stewart toroid
Notation
Stewart notation	P''
Elements
Faces	10 pentagons 10 squares 20+20+10 triangles
Abstract & topological properties
Flag count	480
Orientable	Yes
Genus	1
Properties
Symmetry	(I2(10)×A1)/2, order 10
Flag orbits	48
Convex	No

P'' is a Stewart toroid. Its vertices lie in two parallel planes, making it a prismatoid.

Related polytopes

P'' (red) in P*

A dodecahedron fits snugly into P'' meeting along its Petrie polygon.

P'' can be found as a section of P*. The vertices and edges of P'' are a subset of those of P*, and all but the pentagonal faces of P'' are faces P*. P* can be built then as the outer blend of 1 P'', 2 oriental hats, and 10 Cs.

A dodecahedron can fit in the tunnel of P'', with the two polyhedra touching exactly along a Petrie polygon of the dodecahedron.

References

• Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686-119 36-3.