ITS MODIFICATIONS. 115 



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Class c. Solid angles replaced by three planes 

 resting on the primary edges. 



The new figures would be dodecahedrons with 

 triangular planes. 



The planes resulting from classes b, and c, would 

 produce a great variety of dodecahedral solids ; not 

 any of which, except the rhombic dodecahedron, can 

 be derived from the octahedron according to the law 

 of symmetry. 



Class d. Solid angles replaced by six planes. 

 The new figures would be contained within 24 

 triangular planes. 



Class e. Edges replaced by tangent planes. 



Produces the cube. 



Plane e on P or P', 120 15' 52". 



Class/. Edges replaced by two planes. 



The new figures would be dodecahedrons with 

 triangular planes, appearing as three-sided pyramids 

 on the planes of the tetrahedron. 



if 2 



