English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A convex polyhedron is called monostable if it can rest in stable positiononly on one of its faces. The aim of this paper is to investigate threequestions of Conway, regarding monostable polyhedra, which first appeared in a1969 paper of Goldberg and Guy (M. Goldberg and R.K. Guy, Stability ofpolyhedra (J.H. Conway and R.K. Guy), SIAM Rev. 11 (1969), 78-82). In this notewe answer two of these problems and make a conjecture about the third one. Themain tool of our proof is a general theorem describing approximations of smoothconvex bodies by convex polyhedra in terms of their static equilibrium points.As another application of this theorem, we prove the existence of a convexpolyhedron with only one stable and one unstable point.

A solution to some problems of Conway and Guy on monostable polyhedra