The Stellations of the Icosahedron

Click here if you want to watch the models with a VRML player instead of a X3D player.

Contents

Introduction

In the book The 59 Icosahedra H.S.M. Coxeter presents all possible stellations of the icosahedron according to a set of rules. This page presents these as 3D models so that the reader can investigate them further.

To be able to view and investigate the 3D models you need a X3D player. See note2.

Models of the Stellations

Cell Name1 Edge Name1 X3D2 model Cell Name1 Edge Name1 X3D2 model
A 0 Model B 1 Model
C 2 Model D 3 4 Model
E 5 6 7 Model F 8 9 10 Model
G 11 12 Model H 13 Model
e1 3' 5 Model f1 5' 6' 9 10 Model
g1 10' 12 Model e1 f1 3' 6' 9 10 Model
e1 f1 g1 3' 6' 9 12 Model f1 g1 5' 6' 9 12 Model
e2 4' 6 9 Model f2 7' 8 Model
g2 8' 9' 11 Model e2 f2 4' 6 8 Model
e2 f2 g2 4' 6 9' 11 Model f2 g2 7' 9' 11 Model
D e1 4 5 Model E f1 7 9 10 Model
F g1 8 9 12 Model D e1 f1 4 6' 9 10 Model
D e1 f1 g1 4 6' 9 12 Model E f1 g1 7 9 12 Model
D e2 3 6 7 Model E f2 5 6 8 Model
F g2 10 11 Model D e2 f2 3 6 8 Model
D e2 f2 g2 4 6 9' 11 Model E f2 g2 5 6 9' 11 Model
f1 5' 6' 9 10 Model e1f1 3' 5 6' 9 10 Model
D e1f1 4 5 6' 9 10 Model f1 g1 5' 6' 9 10' 12 Model
e1f1 g1 3' 5 6' 9 10' 12 Model D e1f1 g1 4 5 6' 9 10' 12 Model
f1 g2 5' 6' 8' 9' 10 11 Model e1f1 g2 3' 5 6' 8' 9' 10 11 Model
D e1f1 g2 4 5 6' 8' 9' 10 11 Model f1 f2 g2 5' 6' 7' 9' 10 11 Model
e1f1 f2 g2 3' 5 6' 7' 9' 10 11 Model D e1f1 f2 g2 4 5 6' 7' 9' 10 11 Model
e2 f1 4' 5' 6 7 9 10 Model D e2 f1 3 5' 6 7 9 10 Model
E f1 5 6 7 9 10 Model e2 f1 g1 4' 5' 6 7 9 10' 12 Model
D e2 f1 g1 3 5' 6 7 9 10' 12 Model E f1 g1 5 6 7 9 10' 12 Model
e2 f1 f2 4' 5' 6 8 9 10 Model D e2 f1 f2 3 5' 6 8 9 10 Model
E f1 f2 5 6 8 9 10 Model e2 f1 f2 g1 4' 5' 6 8 9 10' 12 Model
D e2 f1 f2 g1 3 5' 6 8 9 10' 12 Model E f1 f2 g1 5 6 8 9 10' 12 Model
e2 f1 f2 g2 4' 5' 6 9' 10 11 Model D e2 f1 f2 g2 3 5' 6 9' 10 11 Model
E f1 f2 g2 5 6 9' 10 11 Model

Notes

1 For available X3D / VRML plugins for your browser and OS check here.
2 See The 59 Icosahedra for the cell and edge names.

References

Coxeter, H.S.M, P. du Val, H.T. Flather, J.F. Petrie: The Fifty-Nine Icosahedra, Springer Verlag edition (1982)

Links

Last Updated

2005-09-11, 08:55