Periodic Polyhedra in Spaces of Constant Curvature.
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| Title: | Periodic Polyhedra in Spaces of Constant Curvature. |
|---|---|
| Authors: | Duffield, Christina1 (AUTHOR), Freese, Daniel1 (AUTHOR), Holt, William1 (AUTHOR), Weber, Matthias1 (AUTHOR) matweber@iu.edu, Yol, Ramazan1 (AUTHOR) |
| Source: | Discrete & Computational Geometry. Jul2026, Vol. 76 Issue 1, p91-120. 30p. |
| Subjects: | Spaces of constant curvature, Polyhedra, Tessellations (Mathematics), Platonic solids, Curvature |
| Abstract: | We show the existence of families of periodic polyhedra in spaces of constant curvature whose fundamental domains can be obtained by attaching prisms and antiprisms to Archimedean solids. These polyhedra have constant discrete curvature and are weakly regular in the sense that all faces are congruent regular polygons, and all vertex figures are congruent as well. Some of our examples have stronger conformal or metric regularity. The polyhedra are invariant under either a group generated by reflections at the faces of a Platonic solid or a group generated by transformations that are reflections at the faces of a Platonic solid, followed by a rotation about an axis perpendicular to the respective face. In particular, suitable quotients will be compact polyhedral surfaces in (possibly non-compact) spaceforms. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194776510 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00454-025-00764-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 30 StartPage: 91 Subjects: – SubjectFull: Spaces of constant curvature Type: general – SubjectFull: Polyhedra Type: general – SubjectFull: Tessellations (Mathematics) Type: general – SubjectFull: Platonic solids Type: general – SubjectFull: Curvature Type: general Titles: – TitleFull: Periodic Polyhedra in Spaces of Constant Curvature. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Duffield, Christina – PersonEntity: Name: NameFull: Freese, Daniel – PersonEntity: Name: NameFull: Holt, William – PersonEntity: Name: NameFull: Weber, Matthias – PersonEntity: Name: NameFull: Yol, Ramazan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01795376 Numbering: – Type: volume Value: 76 – Type: issue Value: 1 Titles: – TitleFull: Discrete & Computational Geometry Type: main |
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