1894.] On Homogeneous Division of Space. 



FIG. 8. 

 5 5 



13 



tetrakaidekahedron of which the twenty-four corners are the corners 

 of the tetrahedrons thus placed may conveniently be called the orthic 

 tetrakaidekahedron. It has six equal square faces and eight equal 

 equiangular and equilateral hexagonal faces. It was described in 12 

 of my paper on " The Division of Space with Minimum Partitional 

 Area,"* under the name of " plane-faced isotropic tetrakaidekahedron"; 

 but I now prefer to call it orthic, because, for each of its seven pairs 

 of parallel faces, lines forming corresponding points in the two faces 

 are perpendicular to the faces, and the planes of its three pairs of 

 square faces are perpendicular to one another. Fig. 8 represents 

 an orthogonal projection on a plane parallel to one of the four 

 pairs of hexagonal faces. The heavy lines are edges of the tetra- 

 kaidekahedron. The light lines are edges of the tetrahedrons of 

 13, or parts of those edges not coincident in projection with the 

 edges of the tetrakaidekahedron. The figures 1, 1, 1 ; 2, 2, 2 ; . . . ; 

 6, 6, 6 show corners belonging respectively to the six tetrahedrons, 



* ' Phil. Mag.,' 1887, 2nd half-year, and ' Acta Mathematical vol. 11, pp. 121134. 



