### Abstract

We construct new polyhedra such that some of their similar or affine images can be inscribed in (or circumscribed about) every centrally symmetric convex body.

One of the main theorems is as follows. If K is a centrally symmetric, three-dimensional, convex body, then either an affine-regular dodecahedron is inscribed in K or there are two affine-regular dodecahedra D1 and D2 such that nine pairs of opposite vertices of Di, i = 1, 2, lie on the boundary of K. Furthermore, the remaining two vertices of D1 lie outside K, while the remaining two vertices of D2 lie inside K.

One of the main theorems is as follows. If K is a centrally symmetric, three-dimensional, convex body, then either an affine-regular dodecahedron is inscribed in K or there are two affine-regular dodecahedra D1 and D2 such that nine pairs of opposite vertices of Di, i = 1, 2, lie on the boundary of K. Furthermore, the remaining two vertices of D1 lie outside K, while the remaining two vertices of D2 lie inside K.

Original language | English |
---|---|

Pages (from-to) | 552-557 |

Number of pages | 6 |

Journal | Journal of Mathematical Sciences |

Volume | 212 |

Issue number | 5 |

Early online date | 8 Jan 2016 |

Publication status | Published - 2016 |

## Fingerprint Dive into the research topics of 'Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body'. Together they form a unique fingerprint.

## Cite this

Makeev, V. V., & Netsvetaev, N. Y. (2016). Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body.

*Journal of Mathematical Sciences*,*212*(5), 552-557.