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Article

Brandts, Jan ; Cihangir, Apo
Counting triangles that share their vertices with the unit $n$-cube. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 1-12
MSC: 05A15, 52B05 | MR 3204425 | Zbl 1340.52020
Keywords:
$0/1$-triangle; $0/1$-polytope; $0/1$-equivalence
Summary:
This paper is about $0/1$-triangles, which are the simplest nontrivial examples of $0/1$-polytopes: convex hulls of a subset of vertices of the unit $n$-cube $I^n$. We consider the subclasses of right $0/1$-triangles, and acute $0/1$-triangles, which only have acute angles. They can be explicitly counted and enumerated, also modulo the symmetries of $I^n$.
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