Transformation Groups

, Volume 4, Issue 4, pp 329-353

First online:

The size of a hyperbolic Coxeter simplex

  • N. W. JohnsonAffiliated withDepartment of Mathematics and Computer Science, Wheaton College
  • , R. KellerhalsAffiliated withMathematisches Institut, Universität Göttingen
  • , J. G. RatcliffeAffiliated withDepartment of Mathematics, Vanderbilt University
  • , S. T. TschantzAffiliated withDepartment of Mathematics, Vanderbilt University

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We determine the covolumes of all hyperbolic Coxeter simplex reflection groups. These groups exist up to dimension 9. the volume computations involve several different methods according to the parity of dimension, subgroup relations and arithmeticity properties.