Tesselation of the sphere by 12 congruent spherical rhombi.
No, this is not the Healpix tesselation.

circle
unit d

 90  45  90	270  45  90	-45   0  90	 45   0  90
  0  45  90	180  45  90	 45   0  90	135   0  90
 90  45  90	270  45  90	135   0  90	225   0  90
  0  45  90	180  45  90	225   0  90	315   0  90

  0  45  90	 90  45  90	  0 -45  90	 90 -45  90
 90  45  90	180  45  90	 90 -45  90	180 -45  90
180  45  90	270  45  90	180 -45  90	270 -45  90
270  45  90	  0  45  90	270 -45  90	  0 -45  90

 90 -45  90	270 -45  90	 45   0  90	-45   0  90
  0 -45  90	180 -45  90	135   0  90	 45   0  90
 90 -45  90	270 -45  90	225   0  90	135   0  90
  0 -45  90	180 -45  90	315   0  90	225   0  90