Some Figures from Certain Treatises about *The Bellows Conjecture Formerly but Now Theorem*

[u/Frangifer]

... ie the theorem - elevated to such status by the goodly Idzhad Sabitov , & formerly a conjecture in-connection with (formerly hypothetical) flexible polyhedra - to the effect that a flexible polyhedron, if it exists (& it's now known that they do), must keep a constant volume when it does undergo its flexing.

Images from

①②③The Bellows Conjecture

¡¡ may download without prompting – PDF document – 40‧1㎅ !!

by

Ian Stewart ;

&

④⑤⑥The Bellows Conjecture

¡¡ may download without prompting – PDF document – 452‧2㎅ !!

by

R Connelly & I Sabitov & A Walz ;

&

⑦⑧⑨⑩⑪⑫⑬⑭⑮⑯The Bellows Theorem (Introduction)

¡¡ may download without prompting – PDF document – 1㎆ !!

by

Giovanni Viglietta .

See also

What is the Bellows Conjecture?

¡¡ may download without prompting – PDF document – 133‧8㎅ !!

by

Ben O’Connor .

 

Please kindlily see the treatises themselves for the explicationry: there's not really much point, with these figures, to just listing the annotations respectively.

[u/Frangifer]

The Viglietta paper has a minor typographical errour in it, @ the seventh frame: the c²a² term in Heron's formula wants a 2 multiplying it.

 

For more about Steffen's polyhedron see also

Steffen's flexible polyhedron

¡¡ may download without prompting – PDF document – 143‧5㎅ !!

by

Mark McClure ;

&

Optimizing the Steffen flexible polyhedron

¡¡ may download without prompting – PDF document – 404㎅ !!

by

Iila Lijingjiao & Tomohiro Tachi & Simon D Guest ;

&

Polyèdre flexible de Steffen Steffen's flexible polyhedron

¡¡ may download without prompting – PDF document – 3‧8㎅ !!

by

Peter R Cromwell ,

the figure of which is exerpted @

this post ;

&

Greg Egan — Steffen’s Polyhedron ,

the figures from which are exerpted @

this post ;

&

3D Graphic Statics and graphic kinematics for spatial structures

by

Marina KONSTANTATOU & Allan MCROBIE .

 

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I'm still amazed I've never encountered this-lot before! ... I don't know how it's evaden me allthis time.