50 TERMINOLOGY. . 68. 



2. This form contains three kinds of edges ; the first meet 

 in the more acute, the second in the more obtuse equian- 

 gular solid angles, and the third join those which are form- 

 ed by three different plane angles. 



3. Its sections are rhombohedral ; and it does not pos- 

 sess any other but rhombohedral axes, in conformity with 

 the sections. 



4. These solids are remarkable, on account of their being 

 as it were twisted, some to the Right, others to the Left. 

 They are equal and similar to each other ; but every part of 

 the one, has exactly the reverse situation 0f the other. 



5. The dimensions of the three varieties pf this form, are 

 as follows : 



a. b. c. d. 



1. 116 6' 13". 111 50' 44". 93 49' 21". 143 11' 29". 



2. 113 21' 46". 113 43' 28". 99 35' 38". 130 12' 11". 

 & 113 34' 41". 128 20' 44". 97 59' 19". 136 39' 57". 



e. A. B. C. 



1. 75 2' 13 ;; . 141 47' 12". 94 5' 45". 106 36' 2". 



2. 83 6' 57". 131 4' 57". 78 2?' 46". 115 22' 37", 



3. 66 25' 19". 131 48' 37". 95 27' 54". 121 35' 18". 



6. This form has not yet been found in nature ; and the 

 angles of the mentioned varieties depend upon those of the 

 tetraconta-octahedrons, . 77' 134. 



. 68. ICOSITETRAHEDRONS IN GENERAL. 



The Icositetrahedrons are contained under twen- 

 ty-four equal and similar faces, the figure of which 

 determines the kinds of icositetrahedrons. An 

 icositetrahedron, whose faces are triangles, is 

 termed a TVigwiaZ-icositetrahedron ; one whose 

 faces are tetragons, a TWrag-owaZ-icositetrahedron ; 

 and one whose faces are pentagons, a Pentagonal- 

 icositetrahedron. 



