320 APPENDIX CALCULATION OF THE 



THE RHOMBIC DODECAHEDRON. 

 



Its elements. 



The inclination of any two adjacent planes at their 

 common edge zz 120, to be called /,. 

 Obtuse plane angles zz 109 28' 16", may be 

 called A t . 



Acute plane angles zz 70 31' 44", may be 

 called A z . 

 Edges all equal. 



Inclination of edge to edge measured over the 

 summit = 109 28' 16", may be called A 3 . 

 Inclination of plane on plane measured over 

 the summit zz 90. 



Inclination of an edge to the adjacent lesser 

 diagonal zz 125 15' 52", may be called A 4 . 

 Ratio of an edge : ^a greater diagonal ::*3 :*%. 



an edge : \ a lesser diagonal :: *3 : 1. 



an edge : greater axis :: ^3:4. 



an edge : lesser axis :: 1 : 2. 



greater diagonal : greater axis : : ^2 : 2. 



lesser diagonal : lesser axis :: 1 : ^3. 



Its units of comparison. 



For simple and mixed decrements on the acute 

 angles, or on the edges, the unit is zz 1. 



For simple or mixed decrements on the obtuse 



angles, it is , being the ratio of \ a lesser diagonal 



V 3 

 to an edge. 



After the ample illustration which has been given 

 of the methods proposed for determining the laws of 

 decrement, it will not be necessary in future to do 



