## Edgewise subdivision of a simplex.(English)Zbl 0968.51016

The main result of the paper is that, for every positive integer $$k$$, every $$d$$-dimensional simplex can be decomposed into $$k^d$$ simplices of dimension $$d$$, all of the same volume and shape characteristics. The approach is based on an algebraic description of a simplex. The elementary model is very effective in the detailed analysis of the algorithm employed to construct a subdivision of a simplex, and is very convenient for computer representation of simplices and subdivisions.
It is worth mentioning that the same model can be used to decompose a simplex into Cartesian product of simplices [see D. R. Grayson, K-Theory 3, No. 3, 247-260 (1989; Zbl 0701.18007)]. The construction has been also used by T. N. T. Goodman and J. Peters [Comput. Aided Geom. Des. 12, No. 1, 53-65 (1995; Zbl 0875.68829)] to design smooth manifolds.

### MathOverflow Questions:

Triangulation of a simplex

### MSC:

 51M20 Polyhedra and polytopes; regular figures, division of spaces 68U07 Computer science aspects of computer-aided design 52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)

### Keywords:

simplex; subdivision of a simplex; barycentric coordinates

### Citations:

Zbl 0701.18007; Zbl 0875.68829
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