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# On the number of pairwise touching simplices

Lemmens, Bas, Parsons, Christopher (2015) On the number of pairwise touching simplices. Involve: A Journal of Mathematics, 8 (3). pp. 513-520. ISSN 1944-4176. E-ISSN 1944-4184. (doi:10.2140/involve.2015.8.513)

## Abstract

In this note, it is shown that the maximum number of pairwise touching translates of an n -simplex is at least n+3 for n=7 , and for all n?5 such that n?1mod4 . The current best known lower bound for general n is n+2 . For n=2 k ?1 and k?2 , we will also present an alternative construction to give n+2 touching simplices using Hadamard matrices.

Item Type: Article 10.2140/involve.2015.8.513 Q ScienceQ Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QA Mathematics (inc Computing science) > QA440 Geometry Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Bas Lemmens 22 Oct 2014 11:43 UTC 06 Feb 2020 04:10 UTC https://kar.kent.ac.uk/id/eprint/43592 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-6713-7683
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