✦ LIBER ✦
A Lower Bound for the Simplexity of then-Cube via Hyperbolic Volumes
✍ Scribed by Warren D. Smith
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 139 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
✦ Synopsis
Let T (n) denote the number of n-simplices in a minimum cardinality decomposition of the n-cube into n-simplices. For n ≥ 1, we show that T (n) ≥ H (n), where H (n) is the ratio of the hyperbolic volume of the ideal cube to the ideal regular simplex.
Explicit bounds for T (n) are tabulated for n ≤ 10, and we mention some other results on hyperbolic volumes.