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Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature
Published 2015-03-01“…In this work we indicate some special classes of polyhedra for which these polynomials can be found by a sufficiently effective algorithm which also works in spaces of constsnt curvature of any dimension.…”
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Chiral Polyhedra Derived from Coxeter Diagrams and Quaternions
Published 2011-12-01“…In this paper we construct the chiral polyhedra and their dual solids in a systematic way. …”
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Convex-Faced Combinatorially Regular Polyhedra of Small Genus
Published 2011-12-01Subjects: Get full text
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Closed Locally Minimal Networks on the Surfaces of Convex Polyhedra
Published 2013-10-01“…We study such networks on the surfaces of convex polyhedra and discuss the problem of describing the set of all convex polyhedra that have such networks. …”
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Self-Dual, Self-Petrie Covers of Regular Polyhedra
Published 2012-02-01“…The well-known duality and Petrie duality operations on maps have natural analogs for abstract polyhedra. Regular polyhedra that are invariant under both operations have a high degree of both “external” and “internal” symmetry. …”
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Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
Published 2018“…This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques.…”
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Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
Published 2018“…This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques. …”
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Determining the directional contact range of two convex polyhedra
Published 2010“…The directional contact range of two convex polyhedra is the range of positions that one of the polyhedron may locate along a given straight line so that the two polyhedra are in collision. …”
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Extending Goldberg’s method to parametrize and control the geometry of Goldberg polyhedra
Published 2022-08-01Subjects: “…Goldberg polyhedra…”
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CONSIDERATIONS CONCERNING THE REPRESENTATION OF THE INTERSECTIONS OF POLYHEDRA IN VARIOUS SYSTEMS OF REPRESENTATION
Published 2017-05-01Subjects: “…intersections of polyhedra, axonometry, projection with elevations, orthogonal projection on two planes of projection.…”
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CONSIDERATIONS CONCERNING THE REPRESENTATION OF THE INTERSECTIONS OF POLYHEDRA IN VARIOUS SYSTEMS OF REPRESENTATION
Published 2017-05-01Subjects: “…intersections of polyhedra…”
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Architecture design of novel carbon family: Polyhedra as building blocks
Published 2023-06-01Subjects: Get full text
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Some New Symmetric Equilateral Embeddings of Platonic and Archimedean Polyhedra
Published 2018-09-01Subjects: “…polyhedra…”
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CONSIDERATIONS CONCERNING THE REPRESENTATION OF THE INTERSECTIONS OF POLYHEDRA IN VARIOUS SYSTEMS OF REPRESENTATION
Published 2017-05-01Subjects: “…intersections of polyhedra…”
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Atomic descriptors generated from coordination polyhedra in crystal structures
Published 2021-01-01Subjects: Get full text
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