Grasshopper formulation for the snub dodecahedron and the pentagonal hexecontahedron.
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| Title: | Grasshopper formulation for the snub dodecahedron and the pentagonal hexecontahedron. |
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| Authors: | Sanchez-Alvarez, Jaime1,2 (AUTHOR) jaime.sanchez@t-online.de |
| Source: | International Journal of Space Structures. Jun2026, Vol. 41 Issue 2, p117-129. 13p. |
| Subjects: | Polyhedra, Three-dimensional modeling, Visual programming languages (Computer science), Geometrical constructions, Algorithms |
| Abstract: | The purpose of the present paper is to demonstrate how the script components of Grasshopper, the user-programming platform of the geometry program Rhinoceros 7/8, can be used to create a software tool for the generation of two complex semi-regular polyhedra, namely, the snub dodecahedron and its dual, the pentagonal hexecontahedron. The snub dodecahedron is an Archimedean polyhedron whose geometric construction is not as simple or direct as that of other polyhedra. The dual of this polyhedron is the Catalan polyhedron known as the pentagonal hexecontahedron, a convex polyhedron with 60 identical, axially symmetric, semi-regular, pentagonal faces. The intricacy of deriving and specifying the geometric particulars of these two polyhedra might be a reason for their infrequent application in dome-like architectural envelopes, such as the "Amazon Spheres" in Seattle (2018). A numerical method for the geometric specification of the snub dodecahedron based on the regular icosahedron is used in this article to illustrate its formulation in Grasshopper (GH). The successive GH implementation of the duality principle to obtain the pentagonal hexecontahedron completes the formulation exercise. Here, the geometric construction method and its algorithm, as well as the data organization and its handling within the data tree structure in Grasshopper, pose the actual challenge for an efficient formulation. The practical outcome of the present discussion is provided by the GH-script that generates the mentioned polyhedra, which can be used in further design and construction processes. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Space Structures is the property of Sage Publications Inc. 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194579948 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Grasshopper formulation for the snub dodecahedron and the pentagonal hexecontahedron. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Sanchez-Alvarez%2C+Jaime%22">Sanchez-Alvarez, Jaime</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> jaime.sanchez@t-online.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Space+Structures%22">International Journal of Space Structures</searchLink>. Jun2026, Vol. 41 Issue 2, p117-129. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Polyhedra%22">Polyhedra</searchLink><br /><searchLink fieldCode="DE" term="%22Three-dimensional+modeling%22">Three-dimensional modeling</searchLink><br /><searchLink fieldCode="DE" term="%22Visual+programming+languages+%28Computer+science%29%22">Visual programming languages (Computer science)</searchLink><br /><searchLink fieldCode="DE" term="%22Geometrical+constructions%22">Geometrical constructions</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The purpose of the present paper is to demonstrate how the script components of Grasshopper, the user-programming platform of the geometry program Rhinoceros 7/8, can be used to create a software tool for the generation of two complex semi-regular polyhedra, namely, the snub dodecahedron and its dual, the pentagonal hexecontahedron. The snub dodecahedron is an Archimedean polyhedron whose geometric construction is not as simple or direct as that of other polyhedra. The dual of this polyhedron is the Catalan polyhedron known as the pentagonal hexecontahedron, a convex polyhedron with 60 identical, axially symmetric, semi-regular, pentagonal faces. The intricacy of deriving and specifying the geometric particulars of these two polyhedra might be a reason for their infrequent application in dome-like architectural envelopes, such as the "Amazon Spheres" in Seattle (2018). A numerical method for the geometric specification of the snub dodecahedron based on the regular icosahedron is used in this article to illustrate its formulation in Grasshopper (GH). The successive GH implementation of the duality principle to obtain the pentagonal hexecontahedron completes the formulation exercise. Here, the geometric construction method and its algorithm, as well as the data organization and its handling within the data tree structure in Grasshopper, pose the actual challenge for an efficient formulation. The practical outcome of the present discussion is provided by the GH-script that generates the mentioned polyhedra, which can be used in further design and construction processes. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Space Structures is the property of Sage Publications Inc. 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.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1177/09560599261431941 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 117 Subjects: – SubjectFull: Polyhedra Type: general – SubjectFull: Three-dimensional modeling Type: general – SubjectFull: Visual programming languages (Computer science) Type: general – SubjectFull: Geometrical constructions Type: general – SubjectFull: Algorithms Type: general Titles: – TitleFull: Grasshopper formulation for the snub dodecahedron and the pentagonal hexecontahedron. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Sanchez-Alvarez, Jaime IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 09560599 Numbering: – Type: volume Value: 41 – Type: issue Value: 2 Titles: – TitleFull: International Journal of Space Structures Type: main |
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