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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  
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.
 
 Having All Faces Congruent.''  Bull. Research Council Israel 8F, 215-218, 1960.