Forma, Vol. 14 (No. 3), pp. 221-237, 1999
Original Paper

On a General Method to Calculate Vertices of N-dimensional Product-Regular Polytopes

Motonaga Ishii

Graduate School of Human and Environmental Studies, Kyoto University, Yoshida-nihonmatu-cho, Sakyo-ku, Kyoto 606-8501, Japan

(Received February 5, 1999; Accepted August 18, 1999)

Keywords: N-dimensional Regular Polytope, N-dimensional Semi-Regular Polytope, N-dimensional Product-Regular Polytope

Abstract. A set of N-dimensional product-regular polytopes (N-dimensional PRP-set) can be produced from a regular polytope by taking the product space of N solid models which are derived from the boundary figures (vertices, edges, faces, and so on) of the regular polytope.
I found a method to calculate all vertices of the N( 2)-dimensional PRP-set derived from an N-dimensional regular polytope.
The PRP-set derived from a regular polytope is similar to the set of semi-regular polytopes derived from the regular polytope in point of that both include simple semi-regular polytopes which have the same rotational symmetry with the regular polytope. But the PRP-set differs from the set of semi-regular polytopes because that the PRP-set includes the regular polytope itself, and it doesn't include the snub-type semi-regular polytopes, regular prisms, nor regular anti-prisms, all of which have no same rational symmetry with regular polytopes.
In this paper, I calculated and displayed only 2 to 6-dimensional PRP-sets by using computer.

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