( mo ) 



the bounding elements of M^ on the diagonal ; i( is an extension of 

 the second diagram n = 5 of the plate, added to the communication 

 on the section of the measure-polytope Mu of the space >S„ vvitii a 

 central space Sp„-\ Jioi-mal lo a diagonal {Proceedimjs, Jan. 1908). 

 Here, too, we restrict ourselves to a few sections, viz. to the tran- 

 sition forms and to those intermediary forms which bisect the distance 

 of two adjacent transition forms; according to- the notation introduced 



1 

 there, we distinguish the transition forms by the symbols t^U^ 



o 



2 S 4 13 



— Alc,-M,,-M,, the ijitermediarv forms by the symbols --il/j,-— J/., 

 5 ' 5 ' 5 ' * • 10 10 



5 7 9 



— ilA, — M^,— M^. As these sections have I)een incidentally already 

 10 '10 '10 ' 



found in the last quoted paper, we can suflice here by a mere 



enumeration ; to be able to indicate relations in measure we again 



assume that we have taken half the edge of M^ as measure-unit. 



Transition forms. As two sections pM, and qM. of which the 



fractional symbols p and q complete each other to unity, form two 



oppositely orientated positions of the same poly tope, we have here 



1 4 



to deal with but two ti-ansition forms, viz. -M,^ — - J/j and 



o 



2 3 1 (21^2) 



-][J,= M,. Of these - i/, is a regular tivecell C5 , whilst 



5 ' 5 5 



2 



— Ml, is formed (see Proceedin</s, page 488 under n = 6) by trun- 

 5 



eating a tivecell C5 ' at the vertices as far as liall\vay the edges 



and hence transforming it into a polytope (10, 30, 30, 10) with 



edges 2^/2 ; for the last form Proceedings, page 503, can be 



compared. 



1 9 



Intermediary forms. Of the three intermediary forms ^^^1-, ^= — tt. M.^, 



3 7 5 '■\/2 



— M =z -J/, — M, tlie lirst is a C5 ', the second iProceed- 



10 10 ' 10 ' 



C3 V 2) 

 mgs, page 488 under n — 7) a tivecell 6\ truncated as far as 



a third of the edges, passing by this proceeding into a polytope 



(20, 40, 30, 10) with edges \ '2, tlie third {Proceedings, page 487 



under 71 = 5) a cf^ truncated as tar as three tifths of the edges, 

 which has on account of this passed into a polytope (30, 60, 40, 10) 

 with edges 1-/2. 



We shall now pass to diagram 2 where the plane through two 



