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- ...dra are [[polyhedral dual|duals]] of each other. The geodesic and Goldberg polyhedra are parameterized by integers ''m'' and ''n'', with <math>m > 0</math> and ! rowspan=2 | Vertices<br>(geodesic)<br>Faces<br>(Goldberg) ...30 KB (3,871 words) - 13:23, 5 February 2025
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- {{short description|Geodesic polyhedron with 80 faces}} | type = [[Geodesic polyhedron]] (2,0) ...5 KB (664 words) - 01:35, 29 January 2025
- |+ Icosahedral Goldberg polyhedra, {{nobr|with pentagons in red}} ...h]]s of each other. A Goldberg polyhedron is a [[dual polyhedron]] of a [[geodesic polyhedron]]. ...12 KB (1,539 words) - 17:18, 4 February 2025
- | image1 = Geodesic icosahedral polyhedron_example.png | image2 = Geodesic icosahedral polyhedron_example2.png ...17 KB (2,290 words) - 21:24, 4 February 2025
- ...] is a [[Net (polyhedron)|net]] obtained by cutting the polyhedron along [[geodesic]]s (shortest paths) through its faces. It has also been called the '''inwar ...P</math>, in [[general position]], meaning that there is a unique shortest geodesic from <math>p</math> to each [[Vertex (geometry)|vertex]] of <math>P</math>. ...6 KB (747 words) - 07:47, 11 March 2024
- ...th> consists of all points on the surface that have two or more shortest [[geodesic]]s to <math>p</math>. For every convex polyhedron, and every choice of the | title = Continuous blooming of convex polyhedra ...3 KB (436 words) - 07:34, 11 January 2024
- ...dra are [[polyhedral dual|duals]] of each other. The geodesic and Goldberg polyhedra are parameterized by integers ''m'' and ''n'', with <math>m > 0</math> and ! rowspan=2 | Vertices<br>(geodesic)<br>Faces<br>(Goldberg) ...30 KB (3,871 words) - 13:23, 5 February 2025
- ...n (3,1) and geodesic polyhedron (3,1). The Goldberg polyhedra and geodesic polyhedra were precursors to the Goldberg–Coxeter operation. | alt2 = Geodesic polyhedron (3,1) ...21 KB (2,865 words) - 13:23, 8 November 2023
- ...n space into cubes. However, not all polyhedra can be represented as ideal polyhedra – a polyhedron can be ideal only when it can be represented in Euclidean ge Every two ideal polyhedra with the same number of vertices have the same surface area, and it is poss ...27 KB (3,600 words) - 09:46, 9 January 2025
- The [[great icosahedron]] is one of the four regular star [[Kepler-Poinsot polyhedra]]. Its [[Schläfli symbol]] is {3, {{sfrac|5|2}}}. Like the convex form, it ...lations have more than one face in each plane or form compounds of simpler polyhedra. These are not strictly icosahedra, although they are often referred to as ...11 KB (1,541 words) - 20:30, 21 January 2025
- ...tion|Symmetrical transformations of the cuboctahedron into related uniform polyhedra}} ...Koca|Al-Mukhaini|Koca|Al Qanobi|2016|loc=4. Pyritohedral Group and Related Polyhedra|p=145|ps=; see Table 1.}} ...16 KB (2,286 words) - 20:02, 3 November 2024
- ...ons the edges are helices, in the imposed 3-sphere [[topology]] they are [[geodesic]]s and have no [[Torsion of a curve|torsion]]. They spiral around each othe ...University of California Press |isbn=978-0-520-03056-5 |chapter=5. Joining polyhedra §5.36 Tetrahelix |page=53}} ...10 KB (1,315 words) - 22:35, 11 April 2024
- ...appearing as the edges and [[diagonal]]s of [[polygon]]s and [[polyhedron|polyhedra]], line segments also appear in numerous other locations relative to other Beyond Euclidean geometry, [[geodesic segment]]s play the role of line segments. ...11 KB (1,725 words) - 18:23, 15 January 2025
- ...than [[Riemannian manifold]]s, where metric completeness is equivalent to geodesic completeness). * E. Bloch, The angle defect for arbitrary polyhedra, Beiträge zur Algebra und Geometrie, volume 39 (1998), pp.379–393 ...11 KB (1,487 words) - 15:10, 22 June 2024
- ...many developers to further pioneer offshoots from synergetics, especially geodesic dome and dwelling designs. Among Fuller's contemporaries were Joe Clinton ( ...-radius spheres. This tetrahedron anchors a set of concentrically arranged polyhedra proportioned in a canonical manner and inter-connected by a twisting-contra ...22 KB (3,043 words) - 17:13, 29 January 2025