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Abstract
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We prove that alternating links with two totally geodesic
checkerboard surfaces are three links with projection the
–skeleton
of the octahedron, the cuboctahedron and the icosidodecahedron. Then we
characterize these links as right-angled completely realizable links and show that all
hyperbolic weaving knots with two exceptions have both checkerboard surfaces not
totally geodesic.
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Keywords
hyperbolic geometry, alternating link, totally geodesic
surface, right-angled polyhedron
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Mathematical Subject Classification
Primary: 57M50
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Publication
Received: 24 May 2020
Revised: 5 October 2020
Accepted: 20 October 2020
Published: 22 November 2021
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