( 'Mu ) 



III our space \\iv IIicoihmiis hold u'ood : 



1 '. "'riic (Mulil \('i-(i('('s of a ciilx- /*; can l»c an-aiiiivd inio iwo 

 (|iiadni|)l('s of \(Mlic('s not coiiiiccUmI hv cdu-es, or of iion-adjaccnl 



xcrliccs, llic xcrliccs ol Iwo Iclracdcrs /\ 



\'. "'riic ('iulit faces of an oclacdcr /^ can he ai-ran^cd iiilo iwo 

 ((iiadrnplcs of planes (»f w liich no Iwo planes pass ihronuli one 

 and llie same rd'^o, i. e. of (piadniples of non-a<IJaceiil planes, ilie 



faces of Iwo lelraeders I\ 



.(0 



11'^. -''Jlie Iwejily \(M-tices of a /^lo forni laken />r/'rr ihc \«Tlices 

 of li\"e /^G '"HkI )ai<eii (u/cr in Iwo differeiil wa\s llie \-erlices 



rA,:i+i/5)i/o_, 



ot ll\-e / 4 



\\'\ "The Iwcnlv faces of a /'on tonii laken fn-lcc Ihe laces (»f 



L' / 8 



lix'c /'s '^ix' laken r>ii<'r in h\(> wavs llie faces of li\( 



r 



The leiiulh of llie ed^es indicaled for ihe c(niijioneiils follows 

 innnedialelv from ihe ohsei'xalion llial for ihe deconiposilion accordiiii;- 

 lo the \"erlices Ihe radius of ihe circninscrilied sphere, for Ihe 

 (leconi|)()silioji according' lo the faces the ra<liiis of the iiisci-ilie(l 

 sphere r<Mnaiiis nnchan^cd. 



Koi- >S4 we ha\"e the follow iiii;- iheoi-eiiis: 



]II. "'J'lie sixteen \-erlices of a /"'s <*an l>e arranu'ed into two 

 (jclnples of non-adjacent Ncrtices. ihe x'ertices of two sixteeii-cells 



/'*i,5 . In like w a v /V; .uixes acoH'din^ü,- to llie liinitiiiu' s[»aces Iwo 

 ' s 



. ' 1; _ 



1\'. "'Idle twciilv-fonr x'erlices of a /^4 form the lliree oclnples 

 of xcrliccs of three /\i; In like xxax /^^ iiixes accordinu to ihe 



(1/2; ,, 



liniitiiiLi' spaces three /*^ 



V. "The one hundred and Ixxeiilv xerlices of a /Vdd t'oriii in lixe 



-.^n-i-i/r,-,^ I) 



diflcreni xxays the xorlic(>s of fix'e /^4 . In like x\ ay /*io,i uix-es 



accor(liiiL!' lo the liiiiitinu' spaces in lixe xxays jjxc /V, 



