Editing Reuleaux triangle (section)

=== Three-dimensional version === <!-- This section is linked from [[Sphere]] -->
[[File:Reuleaux-tetrahedron-intersection.png|thumb|Four balls intersect to form a Reuleaux tetrahedron.]]
The intersection of four [[ball (mathematics)|balls]] of radius ''s'' centered at the vertices of a regular [[tetrahedron]] with side length ''s'' is called the [[Reuleaux tetrahedron]], but its surface is not a [[surface of constant width]].<ref name=weber>{{citation
  | last = Weber | first = Christof
  | year = 2009
  | url = http://www.swisseduc.ch/mathematik/geometrie/gleichdick/docs/meissner_en.pdf
  | title = What does this solid have to do with a ball?}} Weber also has [http://www.swisseduc.ch/mathematik/geometrie/gleichdick/index-en.html films of both types of Meissner body rotating] as well as [http://www.swisseduc.ch/mathematik/geometrie/gleichdick/meissner-en.html interactive  images].</ref>  It can, however, be made into a surface of constant width, called [[Reuleaux tetrahedron#Meissner bodies|Meissner's tetrahedron]], by replacing three of its edge arcs by curved surfaces,  the surfaces of rotation of a circular arc. Alternatively, the [[surface of revolution]] of a Reuleaux triangle through one of its symmetry axes forms a surface of constant width, with minimum volume among all known surfaces of revolution of given constant width.<ref name="ccg">{{citation
  | last1 = Campi | first1 = Stefano
  | last2 = Colesanti | first2 = Andrea
  | last3 = Gronchi | first3 = Paolo
  | contribution = Minimum problems for volumes of convex bodies
  | title = Partial Differential Equations and Applications: Collected Papers in Honor of Carlo Pucci
  | publisher = Lecture Notes in Pure and Applied Mathematics, no. 177, Marcel Dekker
  | year = 1996
  | pages = 43–55}}.</ref>