Geodesic
Five Spheres in Mutual Contact
Journal for geometry and graphics, Tome 4 (2000) no. 2, pp. 109-114.

Voir la notice de l'article provenant de la source Heldermann Verlag

Consider five mutually tangent spheres having (5 over 2) = 10 distinct points of contact. If O is one of these ten points, we obtain by inversion two parallel planes with three ordinary spheres sandwiched between them. Since these three are congruent and mutually tangent, their centres are the vertices of an equilateral triangle. Analogously, if four congruent spheres are mutually tangent, their centres are the vertices of a regular tetrahedron. A fifth sphere, tangent to all these four, may be either a larger sphere enveloping them or a small one in the middle of the tetrahedral cluster. In this article it will be shown that here are fifteen spheres, each passing through six of the ten points of contact of the five mutually tangent spheres. 
@article{JGG_2000_4_2_a0,
     author = { H. S. M. Coxeter},
     title = {Five {Spheres} in {Mutual} {Contact}},
     journal = {Journal for geometry and graphics},
     pages = {109--114},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2000},
     url = {http://geodesic.mathdoc.fr/item/JGG_2000_4_2_a0/}
}
TY  - JOUR
AU  -  H. S. M. Coxeter
TI  - Five Spheres in Mutual Contact
JO  - Journal for geometry and graphics
PY  - 2000
SP  - 109
EP  - 114
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JGG_2000_4_2_a0/
ID  - JGG_2000_4_2_a0
ER  - 
%0 Journal Article
%A  H. S. M. Coxeter
%T Five Spheres in Mutual Contact
%J Journal for geometry and graphics
%D 2000
%P 109-114
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JGG_2000_4_2_a0/
%F JGG_2000_4_2_a0
 H. S. M. Coxeter. Five Spheres in Mutual Contact. Journal for geometry and graphics, Tome 4 (2000) no. 2, pp. 109-114. http://geodesic.mathdoc.fr/item/JGG_2000_4_2_a0/