sets of four tetrahedra of which any two are mutually inscribed 157 



above that gi\»en the four tetrahedra A^B^C^D^, AJS^C2J^'2,y 

 A^B^CJD^, ABCD, there is a simple construction for XYZT. 



The sets PQRS, SiR^Q^P^, R^SJP^Q^, Q^P^S^R^ are related 

 to one another precisely as are ABCD, D^C\B^A^, C^D^-^^B^y 

 B^A^D^C^, and, with the substitution of one set of generators for 

 the other, have the same relation to XYZT. 



These results were obtained geometrically, and appear to con- 

 stitute a simple geometrical construction for such a set of four 

 mutually inscribed tetrahedra. But they can be readily verified 

 analytically from the formulae by which the configuration is most 

 usually treated. 



