aequationes mathematicae

, Volume 59, Issue 1, pp 55–73

Regular projective polyhedra with planar faces I

  • J. L. Arocha
  • J. Bracho
  • L. Montejano

DOI: 10.1007/PL00000128

Cite this article as:
Arocha, J., Bracho, J. & Montejano, L. Aequ. math. (2000) 59: 55. doi:10.1007/PL00000128

Summary.

This is the first of two papers in which we classify the regular projective polyhedra in \( \Bbb P^3 \) with planar faces. Here, we develop the basic notions; we introduce a new diophantine trigonometric equation, which plays a key role in the classification theorem, relating the combinatorial and geometric parameters of such polyhedra, and conclude with the case in which the polyhedron is an embedded surface.

Copyright information

© Birkhäuser Verlag, Basel, 2000

Authors and Affiliations

  • J. L. Arocha
    • 1
  • J. Bracho
    • 2
  • L. Montejano
    • 3
  1. 1.Instituto de Matemáticas, UNAM, Circuito Exterior, C.U., México D.F., 04510, México, e-mail: arocha@math.unam.mxMX
  2. 2.Instituto de Matemáticas, UNAM, Circuito Exterior, C.U., México D.F., 04510, México, e-mail: jbracho@math.unam.mxMX
  3. 3.Instituto de Matemáticas, UNAM, Circuito Exterior, C.U., México D.F., 04510, México, e-mail: luis@math.unam.mxMX