24 citations · 143 across the 29 of their papers we have counts for
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math.CO2011★ 9 cited
Inscribing a regular octahedron into polytopes
Arseniy Akopyan, Roman Karasev
We prove that any simple polytope (and some non-simple polytopes) in admits an inscribed regular octahedron.
math.CO2011★ 11 cited
Kadets type theorems for partitions of a convex body
Arseniy Akopyan, Roman Karasev
For convex partitions of a convex body we prove that we can put a homothetic copy of into each set of the partition so that the sum of homothety coefficients is . In…
math.MG2011★ 8 cited
On some classical constructions extended to hyperbolic geometry
Arseniy V. Akopyan
We consider some constructions in hyperbolic geometry that are analogous to classical constructions in Euclidean geometry. We show that both Monge's theorem and the theorem on the…