A convex Polyhedron with symmetries acting transitively on its faces. Every isohedron has an Even number of faces (Grünbaum 1960).
References
Grünbaum, B. ``On Polyhedra in Having All Faces Congruent.'' Bull. Research Council Israel 8F, 215-218, 1960.
Grünbaum, B. and Shepard, G. C. ``Spherical Tilings with Transitivity Properties.''
In The Geometric Vein: The Coxeter Festschrift (Ed. C. Davis, B. Grünbaum, and F. Shenk). New York: Springer-Verlag, 1982.