
Page 1  Introduction and Backgrounds 

Page 2  Polygons and surfaces 

Page 3  Nest, Polyhedra, SF's, Units 

Page 4  The 34 different nests 

Page 5  Animation of the 34 nests, grouped per kind of polygon: 

Page 6  How can a nest be constructed in a given (closed) polygon: 

Page 7  From nest to polyhedron to spacefiller: example SF #1. 

Page 8  From Spacefiller to Unit to 3DTiling: 

Page 9  Showing the dual network of the last animation: 

Page 10  6 Different variations of this Spacefiller #1: 

Page 11  A more complicated example: Polyhedra of Spacefiller #41: 

Page 12  From Polyhedra to SF for #41: 

Page 13  Make a 3Dtiling: One, two, four and eight SF blocks, copied in 3 directions along rhombohedron raster. 

Page 14  One more example of a 3D tiling: SF #14 

Page 15  The 54 different Polyhedra 

Page 16  The 42 different Spacefillers 

Page 17  All the 16 SF’s made by one kind of nest. 

Page 18  SF animations of SF01SF14 

Page 19  SF animations of SF15SF28 

Page 20  SF animations of SF29SF42 

Page 21  ZPatterns of nests 

Page 22  Some statistics and the structuregraph 

Page 23  3 Tables with details of: Spacefillers, Polyhedra and Nests 

Page 24  Projections of Dual Nets (SF# 1,28,41) 

Page 25  Credits and Acknowledgements 


 Collection of Spacefillers (SF’s)
 Based on this book by Peter Pearce (1978), chapter 8.
 Spidronisation of these SF’s gives some new insights into 3D tilings.
 More details can be found in our paper published in the Bridges 2009 Conference Proceedings, or click here.




Faces of Saddle Polyhedra can be defined with Skew Polygons. 


These can be filled with a minimal surface like a soap film, as Pearce did. 


Or with Spidronnests. This introduces an orientation: CW or CCW (clockwise / counterclockwise) 





In general: Nests are the building blocks of Polyhedra, which can be assembled into SF’s, and to (possibly bigger) periodical Units.
Matching nests in the 3D tiling need to have opposite orientations.





Grey: flat
Blue: regular
Red: mirror 4gon
Purple: mirror 5gon
Turquoise: mirror 6gon
Violet: mirror 8gon
Green: mirror 12gon
Yellow: enantiomorphic







Method: “scale and rotate”. Nest in general not foldable. 



Spidronnest orientations causes doubling compared to Pearce’s SF’s. 





Cyan is CCW and Blue is CW. Projection along raster gives 2Dtilings. 
















(SF’s 1 2 3 4 / 6 9 11 13 / 14 23 24 27 / 28 30 33 39 ) 

















 Thanks to Peter Pearce, who described in his great book “Structure in Nature is a Strategy for Design” all the original Spacefillers, based on saddlesurfaces.
 Thanks to all other members of the Spidron Team (amongst others: Lajos Szilassi, Rinus Roelofs, Marc Pelletier, Amina BuhlerAllen), for all their inspiring earlier work, including four earlier designs of Spidronised Spacefillers.
(SF’s 2 , 3 , 4 and 5, all based on only regular skew polygons)
 Thanks to András Fodor, who made this presentation.
 Apart from the abovementioned contributions, all work presented here was made by:
Walt van Ballegooijen, Paul Gailiunas and Dániel Erdély, 2009.
 For more information about Spidrons, see the main website:
www.spidron.hu.


