Discrete & Computational Geometry

, Volume 13, Issue 3, pp 573–583

Polytopes that fill ℝn and scissors congruenceand scissors congruence

  • J. C. Lagarias
  • D. Moews

DOI: 10.1007/BF02574064

Cite this article as:
Lagarias, J.C. & Moews, D. Discrete Comput Geom (1995) 13: 573. doi:10.1007/BF02574064


Suppose thatP is a (not necessarily convex) polytope in ℝn that can fill ℝn with congruent copies of itself. Then, except for its volume, all its classical Dehn invariants for Euclidean scissors congruence must be zero. In particular, in dimensions up to 4, any suchP is Euclidean scissors congruent to ann-cube. An analogous result holds in all dimensions for translation scissors congruence.

Copyright information

© Springer-Verlag New York Inc. 1995

Authors and Affiliations

  • J. C. Lagarias
    • 1
  • D. Moews
    • 2
  1. 1.AT & T Bell LaboratoriesMurray HillUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA