Geodesic
Equivariant Maps and Some Problems of the Geometry of Convex Sets
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 83-97

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Methods of equivariant topology are applied to some problems of convex set geometry. In particular, it is proved that a pyramid homothetic to a regular pyramid of certain type with a regular $p$-gon as the base, where $p$ is an odd prime, can be inscribed in any convex $(p+5)/2$-dimensional body. 
@article{TM_2002_239_a4,
     author = {A. Yu. Volovikov},
     title = {Equivariant {Maps} and {Some} {Problems} of the {Geometry} of {Convex} {Sets}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {83--97},
     publisher = {mathdoc},
     volume = {239},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_239_a4/}
}
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A. Yu. Volovikov. Equivariant Maps and Some Problems of the Geometry of Convex Sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 83-97. http://geodesic.mathdoc.fr/item/TM_2002_239_a4/