Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body

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Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body. / Makeev, V. V. ; Netsvetaev, N. Yu. .

In: Journal of Mathematical Sciences, Vol. 212, No. 5, 2016, p. 552-557.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{4a28bbc14fe74067bc31d29d561d6512,

title = "Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body",

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.",

keywords = "Convex Body, Similar Image, Symmetric Convex, Symmetric Convex Body, Opposite Vertex",

author = "Makeev, {V. V.} and Netsvetaev, {N. Yu.}",

note = "Makeev, V.V., Netsvetaev, N.Y. Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body. J Math Sci 212, 552–557 (2016). https://doi.org/10.1007/s10958-016-2687-3",

year = "2016",

language = "English",

volume = "212",

pages = "552--557",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body

AU - Makeev, V. V.

AU - Netsvetaev, N. Yu.

N1 - Makeev, V.V., Netsvetaev, N.Y. Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body. J Math Sci 212, 552–557 (2016). https://doi.org/10.1007/s10958-016-2687-3

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Convex Body

KW - Similar Image

KW - Symmetric Convex

KW - Symmetric Convex Body

KW - Opposite Vertex

UR - https://link.springer.com/article/10.1007/s10958-016-2687-3

M3 - Article

VL - 212

SP - 552

EP - 557

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 37560302