The paper shows that no origin-symmetric convex polyhedron in R^3 is the intersection body of a star body. It is shown also that every origin-symmetric convex body in R^d, for d = 3 and 4, can be seen as the intersection body of a star-shaped set whose radial function satisfies conditions related to suitable non-integer Sobolev classes.
Campi, S. (1999). Convex intersection bodies in three and four dimensions. MATHEMATIKA, 46(91), 15-27 [10.1112/s002557930000752x].
Convex intersection bodies in three and four dimensions
CAMPI S.
1999-01-01
Abstract
The paper shows that no origin-symmetric convex polyhedron in R^3 is the intersection body of a star body. It is shown also that every origin-symmetric convex body in R^d, for d = 3 and 4, can be seen as the intersection body of a star-shaped set whose radial function satisfies conditions related to suitable non-integer Sobolev classes.
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https://hdl.handle.net/11365/22004
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