2
views
0
recommends
+1 Recommend
0 collections
0
shares
• Record: found
• Abstract: found
• Article: found
Is Open Access

# The infimum of the volumes of convex polytopes of any given facet areas is 0

Preprint

Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

### Abstract

We prove the theorem mentioned in the title, for $${\mathbb{R}}^n$$, where $$n \ge 3$$. The case of the simplex was known previously. Also, the case $$n=2$$ was settled, but there the infimum was some well-defined function of the side lengths. We also consider the cases of spherical and hyperbolic $$n$$-spaces. There we give some necessary conditions for the existence of a convex polytope with given facet areas, and some partial results about sufficient conditions for the existence of (convex) tetrahedra.

### Most cited references8

• Record: found

### Simplices of maximal volume in hyperbolic n-space

(1981)
Bookmark
• Record: found

### Geometry of Spaces of Constant Curvature

(1993)
Bookmark
• Record: found

### Volume increasing isometric deformations of convex polyhedra

(1996)
Bookmark

### Author and article information

###### Journal
2013-04-24
2014-10-21
10.1556/SSc.Math.2014.1292
1304.6579