1863.] 343 



determine the numbers in the Table A, without complete Tables A, 

 B, C, D of inferior polyedra. 



Registration of the ^-edron 4-acron. 



(Fide arts. XXXI. &c. of my memoir "On the Theory of the Poly- 

 edra," Phil. Trans. 1862.) 



Table A. 



One zoned tetrarchaxine, having principal polar triaces and trian- 

 gles, and amphigrammic secondary axes (art. XXI.).. The zone is 

 *Z={2.1j 2.1,, 0,0,}. 



Table B. 

 Janal polar zoned edge : 



<33)L08=1, 4 Z={2. V 21,, ft,, <U. 



Table C. 

 Zoned radical tetrarchipolar face : 



(3)3^13=1, <z={2.i p 2.1 P , OAJ. 



The 4 prefixed to 3 shows that it is a tetrarchaxiae pole : the 3 

 suffixed shows that the summits of the polar triangle are triaces. It 

 is only in the case of polar triangles that we require, for purposes of 

 construction hereafter, an account of summits about a polar face. 



Table D. 

 Polar zoned edge : 



(88)2^02=1, Z=Z'={2, 2, 0,, 0,}. 



This is the edge above recorded in Table B. 



The summit reciprocal to the face in Table C is the one required 

 to complete that Table. The reciprocal of any face is written by ex- 

 changing faces for summits, and zonal for epizonal edges, in all the 

 signatures. Hence the summit of the 4-edron is 



Registration of the b-edron 5-acron. 



Table A. 

 One 4-zoned monaxine heteroid, the 4-gonal pyramid. 



Table C. 

 Zoned polar face : 



O 4=1 > Z={l p +2.1,l p ,0 3 - 1 }. 

 Z'= {!,!,+ 2.1, 0"}. 



2 c 2 



