16 ANALYTICAL TREATMENT OE THE POLYTOPE3 REGULARLY 



Jc = 1 , last syllable [0] 



(544332), — (54433) (21) — (5443) (322), (5443) (32) (21), (5443) 

 (221), — (544) (3322), (544) (332) (21), (544) (3222), (544) (322) 

 (21), (544) (32) (221), (544) (2221), — (54) (43322), (54) (4332) 

 (21), (54) (433) (221), (54) (43) (3222), (54) (43) (332) (21), (54) 

 (43) (32) (221), (54) (33222), (54) (3322) (21), (54) (332) (221), (54) 

 (32221), — (443322), — (44332) (21), — (4433) (221), — (443) 

 (3222), (443) (322) (21), (443) (32) (221), — (433222), — (43322) 

 (21), — (4332) (221), — (433) (2221), —(43) (32221), — (332221) 



h = 2, last syllable [10] 



(54433), — (5443) (32), — (544) (322), (544) (322), — (54) (4332), 

 (54) (43) (322), — (44332), — (443) (322), — (43322), — (43) 

 (3222), — (33222) 



k = 3, last syllable [210] 



(5443), — (544) (32), — (54) (433), (54) (43) (32), — (4433), — 

 (443) (32), — (4332), — (43) (32 2), — (3322) 



£ = 4, last syllable [2210] 

 (544), — (54) (43), — (443), — (433), — (43) (32), — (332) 



k = 5, last syllable [22210] 

 (54), — (43) 



/•=6, only syllable [322210]. 



We remark, that in general the k of the theorem indicates how 

 many of the axes of the rectangular sj/steni of coordinates are 

 parallel to the space 8 G bearing the (1\. For d = n — 1 , i. e. if 

 we determine the limits of the highest number of dimensions, the 

 k is at the same time the index of the symbol g h indicating the 

 import. For comparison we put side by side in the next table the 

 different g u of the polytope (i J ) 10 just treated and those of its 

 polytope of vertex import 



(,5443322210) g Q 



(544332221)[0] g x 



(54433222) [10] g 2 



(5443322) [2 10] g 3 



(544332)[2210] r h 



(54433)[22210] g 5 



(5443) [3222 10] }/ 6 



(544) [33222 10] y 7 



(54)[43322210] g s 



[443322210] \r h 



(544332221) . g 8 



(54433222)(10) g n 



(5443322) (2 10) g 6 



(544332) (22 10) g h 



(54433)(22210) g x 



(5443) (3222 10) // 3 



(544) (33222 10) g. 2 



(54) (433222 10) g i 



(443322210) . . . . g 



