Accession Number:

AD0687267

Title:

HARMONIC POLYHEDRA

Descriptive Note:

Corporate Author:

ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD

Personal Author(s):

• Giese, John H.
• Masaitis, Ceslovas

Report Date:

1969-03-01

Pagination or Media Count:

25.0

Abstract:

A polyhedron of genus p is harmonic if the number of its faces vertices is the harmonic mean of its numbers of its edges and vertices faces . The determination of all permissible combinations of numbers of vertices, edges, and faces is reduced to solution of Pells equation. Realizations of all such polyhedra with p 1 are described, as well as for all negative p with large enough numbers of edges.

Descriptors:

• *GEOMETRY
• *NUMBER THEORY
• ALGEBRAIC TOPOLOGY
• GEOMETRIC FORMS
• INEQUALITIES

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE