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On rainbow isosceles \(n\)-simplexes. (English) Zbl 1498.52023

The paper is dedicated to geometric problems connected with various colorings of all points of an Euclidean space \(\mathbb{R}^n\) for certain types of \((n+1)\)-colorings of space. It is proved that there are continuum many “rainbow” isosceles \(n\)-simplexes in \(\mathbb{R}^n\).

MSC:

52B45 Dissections and valuations (Hilbert’s third problem, etc.)
51M04 Elementary problems in Euclidean geometries
51M20 Polyhedra and polytopes; regular figures, division of spaces
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