Bibliografia

1

Peter Hilton, Jean Pedersen, ``Build Your Own Polyhedra'', Addison Wesley (1988).

2

Jean J. Pedersen, 1973, ``Plaited Platonic Puzzles'', College Math Journal 4 N $^{\protect \underline{\mbox{\protect \footnotesize o}}}$3, 22-37.

3

http://www.geom.umn.edu/docs/doyle/mpls/handouts/node19.html

4

Denis Weaire (ed.) ``The Kelvin Problem, foam structures of minimal surface area'', Taylor & Francis (1996) ISBN: 0-748-0632-8.

5

http://www.math.lsa.umich.edu/~hales/countdown/, Tamas Hausel, Endre Makai, Andras Szucs, 2000, ``Inscribing cubes and covering by rhombic dodecahedra via equivariant topology'' a publicar.

6

Ver o ficheiro kelvin-9tile-transp.html na directoria http://www.geom.umn.edu/graphics/pix/Special_Topics/Tilings/. Denis Weaire, Robert Phelan, 1994, ``A counterexample to Kelvin's conjecture on minimal surfaces'' Phil. Mag. Lett. 69 107-110.

7

Ver a página 161 do livro ``The Penguin Dictionary of Curious and Interesting Geometry'' de David Wells (1991) que mostra o icosaedro ortogonal de Jessen, também pontualmente flexível. Michael Goldberg, 1978, ``Unstable Polyhedral Structures'', Mathematics Magazine 51 N $^{\protect \underline{\mbox{\protect \footnotesize o}}}$3, 165-170. Walter Wunderlich, 1979, ``Snapping and Shaky Antiprisms'', Mathematics Magazine, 52 N $^{\protect \underline{\mbox{\protect \footnotesize o}}}$4, 235-236.

8

Robert Connelly, I. Sabitov, A. Walz, 1997, ``The Bellows Conjecture'', em ``Contributions to Algebra and Geometry'', 38 N $^{\protect \underline{\mbox{\protect \footnotesize o}}}$1, 1-10.

9

Cauchy, 1813, Second Mémoire, J. École Polytechnique, 9 87, os poliedros convexos não podem ser flexíveis.

10

Robert Connely, 1979, ``How to Build a Flexible Polyhedral Surface'', em ``Geometric Topology'' Proceedings of the 1977 Georgia Topology Conference (Athens, Georgia), edit. James C. Cantrell, Academic Press, 675. Robert Connely, 1979, ``The Rigidity of Polyhedral Surfaces'', Mathematics Magazine, 52 N $^{\protect \underline{\mbox{\protect \footnotesize o}}}$5, 275-283.

11

http://www.sgi.com/grafica/huffman/. David A. Huffman, 1976, ``Curvature and creases: A primer on paper'', IEEE Trans. Comput. C-25, 1010-1019

$\parbox{71mm}{ \begin{flushleft} \epsf... ... la\-te\-rais triangulares equil{\'a}teras.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...r{\^a}mide da figura \protect \ref{phtpbq}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...r{\^a}mide da figura \protect \ref{phtpbq}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...ir{\^a}mide da figura \protect \ref{phtpbq}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...faces laterais triangulares equil{\'a}teras.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...b{\'e}m a figura \protect \ref{paulinhas}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ... poliedro da figura \protect \ref{phtdpbp}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...o respeite as \lq\lq Dist{\^a}ncias'' indicadas.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...enor {\^a}ngulo de (c) e (j) {\'e} $\pi/6$.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...Planifica{\c c}{\ a}o proposta para o cubo.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...formado em que as faces s{\ a}o losangos .} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...myfigure} \textup{Cubo para exerc{\'\i}cio.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ... em que quatro das faces s{\ a}o losangos.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ... a defini{\c c}{\ a}o de v{\'e}rtice plano.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...liedro possui tr{\^e}s v{\'e}rtices planos.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...edro a que foram cortados os v{\'e}rtices.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...sentado na figura \protect \ref{phtnonrec}).} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...extup{Planifica{\c c}{\ a}o de um octaedro.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...permite construir dois poliedros diferentes.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...c c}{\ a}o da figura \protect \ref{plnptq}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...es centradas e o correspondente cuboctaedro.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...encontra na figura \protect \ref{phtnonrec}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...tando o da figura \protect \ref{phtnonrec}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...tical e os outros {\\lq a} volta na horizontal.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...s de espinela ($\mbox{MgAl}_2\mbox{O}_4$).} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...s, pode simplificar a planifica{\c c}{\ a}o.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...tri{\^a}ngulos equil{\'a}teros pelas bordas.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...ompletamente exterior ao volume do poliedro.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...ide de lados is{\'o}sceles rect{\^a}ngulos.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...ra \lq\lq normal'' n{\ a}o foram representadas.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ... si. $1/4$ de v{\'e}rtices n{\ a}o-planos.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...de $2\pi$ rad, ou seja, n{\ a}o existiria.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...extup{$1/6$ de v{\'e}rtices n{\ a}o-planos.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...anos. Poliedro de 72 faces baseado no cubo.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...s v{\'e}rtices planos durante esse processo.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ... deste poliedro possuem $\Theta=3\pi$ rad.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ... \begin{myfigure} \textup{Disfen{\'o}ide.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...ngulos: $\theta$ (entre EB e o plano $xy$).} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...nifica{\c c}{\ a}o de um poliedro toroidal.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...ica{\c c}{\ a}o com arestas mal calculadas.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...poliedro da figura \protect \ref{plnflex}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...vo de Adist em fun{\c c}{\ a}o de $\theta$.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...,12,17), (10,10,11), (12,12,11) e (5,10,12).} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ...liedro da figura \protect \ref{plnmercedes}.} \end{myfigure} \end{flushleft} }$ $\parbox{71mm}{ \begin{flushleft} \epsf... ... com uma aresta curva baseado no tetraedro.} \end{myfigure} \end{flushleft} }$