Draft:Isoaxis
 | Review waiting, please be patient.
This may take 4 months or more, since drafts are reviewed in no specific order. There are 4,482 pending submissions waiting for review.
Where to get help
How to improve a draft
You can also browse Wikipedia:Featured articles and Wikipedia:Good articles to find examples of Wikipedia's best writing on topics similar to your proposed article. Improving your odds of a speedy review To improve your odds of a faster review, tag your draft with relevant WikiProject tags using the button below. This will let reviewers know a new draft has been submitted in their area of interest. For instance, if you wrote about a female astronomer, you would want to add the Biography, Astronomy, and Women scientists tags. Editor resources
Reviewer tools
|
 | This is a draft article. It is a work in progress open to editing by anyone. Please ensure core content policies are met before publishing it as a live Wikipedia article. Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL Last edited by Fsck awk (talk | contribs) 2 months ago. (Update)
This draft has been submitted and is currently awaiting review. |
 | This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these messages)
|
| Isoaxis | |
|---|---|
 | |
| Faces | 60 |
| Edges | 102 |
The IsoAxis (US 3302321) is a geometric net consisting of sixty isosceles triangles that, when scored and folded, forms a movable three-dimensional ring capable of continuous inversion. The structure serves as the geometric basis for a class of dynamic polyhedra known as kaleidocycles. It was discovered by Wallace Walker in 1958 during a project focused on developing structural configurations for paper.
Description and mechanics
[edit]The IsoAxis net is composed of a two-dimensional grid of isosceles right triangles. When the ends of the folded strip are joined, it creates a flexible closed-loop mechanism. The structure can undergo a continuous turning motion around its center axis, cycling through different geometric configurations. Diagrams and assembly instructions for the mechanism are documented in geometric literature.
A detailed guide on constructing the Isoaxis is available in Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination. [1]
History
[edit]Following his initial design, Walker collaborated with mathematician Doris Schattschneider to analyze and catalog variations of the mechanism. This research resulted in the development of an entire family of related dynamic polyhedra, including hexagonal, starred, oblique, and square kaleidocycles. The term "kaleidocycle" was coined to describe these three-dimensional forms, combining the Greek words for "beautiful", "form", and "ring" or "circle".[2]
Schattschneider's work mathematically mapped the periodic tessellations of Dutch artist M. C. Escher onto the deformable surfaces of the IsoAxis grid.[2][3] While linked chain structures made of rigid tetrahedra had been studied previously, Walker's design derived a fully rotational three-dimensional mechanism from a single, flat, continuous grid sheet via its diagonal scores.
In structural origami literature, the IsoAxis is studied alongside other rigid and flexible tessellations, such as the Miura ori, due to its distinct kinematic properties.
References
[edit]- ^ Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination. United Kingdom: Springer New York. 2013. ISBN 9780387927145.
- ^ a b Schattschneider, Doris; Walker, Wallace (1977). M.C. Escher Kaleidocycles. Taschen. ISBN 978-0906212288.
- ^ "Book Review: Art Meets Math in 'Kaleidocycles'". The Los Angeles Times. 27 May 1988.
External links
[edit]- IsoAxis
- The kaleidohedron from the IsoAxis grid
- https://web.archive.org/web/20090123112151/http://www.miura-ori.com/English/e-index.html