Editing Tensegrity (section)

=== Tensegrity prisms ===

The three-rod tensegrity structure (3-way prism) has the property that, for a given (common) length of compression member "rod" (there are three total) and a given (common) length of tension cable "tendon" (six total) connecting the rod ends together, there is a particular value for the (common) length of the tendon connecting the rod tops with the neighboring rod bottoms that causes the structure to hold a stable shape. For such a structure, it is straightforward to prove that the triangle formed by the rod tops and that formed by the rod bottoms are rotated with respect to each other by an angle of 5π/6 (radians).<ref name="RWBurkhardt2008">
{{citation |last= Burkhardt |first=Robert William Jr. |year=2008 |title=A Practical Guide to Tensegrity Design |url=https://www.angelfire.com/ma4/bob_wb/tenseg.pdf |archive-url=https://web.archive.org/web/20041220180510/http://www.angelfire.com/ma4/bob_wb/tenseg.pdf |archive-date=2004-12-20 |url-status=live}}</ref>

The stability ("prestressability") of several 2-stage tensegrity structures are analyzed by Sultan, et al.<ref name="Sultan2001">
{{cite journal |last=Sultan |first=Cornel |author2=Martin Corless |author3=Robert E. Skelton |title=The prestressability problem of tensegrity structures: some analytical solutions |journal=International Journal of Solids and Structures |url=http://www.aoe.vt.edu/people/webpages/csultan/publications-pdfs/journalarticleijss2001.pdf |year=2001 |volume=26 |page=145  |archive-url=https://web.archive.org/web/20151023184609/http://www.aoe.vt.edu/people/webpages/csultan/publications-pdfs/journalarticleijss2001.pdf |archive-date=23 October 2015}}</ref>

The T3-prism (also known as Triplex) can be obtained through form finding of a straight triangular prism. Its self-equilibrium state is given when the base triangles are in parallel planes separated by an angle of twist of π/6. The formula for its unique self-stress state is given by,<ref>{{Cite journal |last1=Aloui |first1=Omar |last2=Flores |first2=Jessica |last3=Orden |first3=David |last4=Rhode-Barbarigos |first4=Landolf |date=2019-04-01 |title=Cellular morphogenesis of three-dimensional tensegrity structures |url=https://www.sciencedirect.com/science/article/pii/S0045782518305814 |journal=Computer Methods in Applied Mechanics and Engineering |language=en |volume=346 |pages=85–108 |doi=10.1016/j.cma.2018.10.048 |issn=0045-7825|arxiv=1902.09953 |bibcode=2019CMAME.346...85A |s2cid=67856423 }}</ref><math display="block">\omega = \omega_1 [-\sqrt{3}, -\sqrt{3}, -\sqrt{3}, \sqrt{3}, \sqrt{3}, \sqrt{3}, 1, 1, 1, 1, 1, 1]^T</math>Here, the first three negative values correspond to the inner components in compression, while the rest correspond to the cables in tension.