SYMMETRY OF SECONDARY PLANES. 



37 



The rhombic Dodecahedron (. 36.) has all its edges similar, and 

 situated at an equal distance from the centre ; but its angles are of 

 two kinds, six formed of four plane angles, and eight of three plane 

 angles. Agreeably to our proposition then, all its edges will un- 

 dergo a similar modification at once, while only a part of its solid 

 angles will be subject to the same replacement. Accordingly, 



Fig. 65, exhibits the rhombis Dodecahedron, with "its edges re- 

 placed by tangent planes, 



Fig. 66, the same, with its edges replaced by two planes. 



Fig. 65. 



Fig. 66. 



Fig. 67, the same, with its obtuse solid angles replaced by tan- 

 gent planes. 



Fig. 68, the same, with its acute solid angles replaced by tangent 

 planes. 



Fig. 67. 



Fig. 68. 



The similar edges and angles of the different Octahedrons have 

 been sufficiently described in our account of these solids (. 35, 37, 

 38, 39) ; the modifications they undergo are regulated by this sim- 

 ilarity, as may be seen in the examples here given. 



