Download presentation

Presentation is loading. Please wait.

Published byFaith Kirk Modified over 4 years ago

1
Part III: Polyhedra c: Cauchys Rigidity Theorem Joseph ORourke Smith College

2
Outline: Reconstruction of Convex Polyhedra zCauchy to Sabitov (to an Open Problem) yCauchys Rigidity Theorem yAleksandrovs Theorem ySabitovs Algorithm

3
zgraph zface angles zedge lengths zface areas zface normals zdihedral angles zinscribed/circumscribed Reconstruction of Convex Polyhedra Steinitzs Theorem Minkowskis Theorem }

5
zgraph zface angles zedge lengths zface areas zface normals zdihedral angles zinscribed/circumscribed Reconstruction of Convex Polyhedra Cauchys Theorem }

6
Cauchys Rigidity Theorem zIf two closed, convex polyhedra are combinatorially equivalent, with corresponding faces congruent, then the polyhedra are congruent; zin particular, the dihedral angles at each edge are the same. Global rigidity == unique realization

7
Same facial structure, noncongruent polyhedra

8
Spherical polygon

9
Sign Labels: {+,-,0} zCompare spherical polygons Q to Q zMark vertices according to dihedral angles: {+,-,0}. Lemma: The total number of alternations in sign around the boundary of Q is 4.

10
The spherical polygon opens. (a) Zero sign alternations; (b) Two sign alts.

11
Sign changes Euler Theorem Contradiction Lemma 4 V

12
Flexing top of regular octahedron

Similar presentations

Presentation is loading. Please wait....

OK

The Other Polyhedra Steven Janke Colorado College.

The Other Polyhedra Steven Janke Colorado College.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on 9/11 conspiracy essay Ppt on micro controller traffic light Ppt on product advertising templates Ppt on self awareness exercises Ppt on single phase and three phase dual converter Ppt on operation research simplex method Ppt on non ferrous minerals in water Mobile ip seminar ppt on 4g Scrolling message display ppt online Ppt on business planning process