$$$$)(c)1999 Inspiration Software, Inc. 6.0 ^ |!5$*ZHH(FG(HH(d'`:d:d(   |YH6!R(BBFFF(TEABXBXFFF****)c.$$$$cccc [;">+S+S0T+S7]IH+S;W;W+S+U:d0S0S0P0S0S0S(00:9[Z"7<p8[+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S+S?Z?ZOYE0O<AaAaNMJ2ZF Math1.inl'gt6tF,S+S   %Fz@kcc9 '' Euler's Formula&H'hZ  Za\+S  \  TT\)t&4&@%x*''&D'h*''&P O Examine, explore, and describe similarities and differences between the models. E Explore relationships and patterns among faces, edges, and vertices. &   Question: If you know only pieces of information (i.e., edges, vertices), can you determine the number of the third (i.e., faces)? &Y   Questions: How do you know this to be true? Will it work for any three-dimensional model?&  Task: Develop a tool that will help someone describe a three-dimensional model if only two of the attributes for the model are known.''h pC+S  @U$&L%L&U ! Explore polyhedra at this site: http://mathforum.org/alejandre/applet.polyhedra.html'&Hjxi|yjxiyy  .H |ywj__y|  ( )  Tetrahedron&T'lskwslshs  ) kwslXXsk '% Cube)`'oW}kWP  .D s|k^^  &X%  Octahedron)d&Tj|r~<||~o  . r~s<|``r  '%H  Dodecahedron( )`l"kwyM"hy  . kwyM__yk  &`%  Icosahedron')do$lx|[o$?i|  ) lx|f[o]]|l  (%@  Buckyball&l( g~z~ Px+S  Lj}\&d%8 '%4'% '%D| Find a relationship between the Edges, Vertices, and Faces. This relationship is called Euler's Formula (pronounced Oiler).  > Write your relationship here: ________________________________ &'j=`g.T+S  ,Q?_55N ((%X )h%T &h% (% 'H%0  Vertices = Edges =  Faces =  &&llB B k_)R+S  'O55L &%, &%( &%$ '4% '(%  Vertices = Edges =  Faces =  'L&o8yWI)R+S  'O9|U55L ',% &% '8% & % '<%  Vertices = Edges =  Faces =  &&j?^ )R+S  'O@\55L &% 'X% 'D$ &$ 'P$  Vertices = Edges =  Faces =  ''LmLLu )R+S  'O 55L '$ &$ &$ '$ & $  Vertices = Edges =  Faces =  )&o3R )R+S  'O4P55L '$$ &$$ '$ &($ '\$  Vertices = Edges =  Faces =  $'i2.2zUHm+S  Ei1}e BB0%$B Find the number of vertices, edges, and faces for each polyhedron.$)i8Ds 8Dc+S+S  +Ss $gc+S+S  +ScssS$$`$ Created by Milly Higgins - 2003)l$ L1y) $ *IXT) $ N\)WUV UU % $ ANL %l$ sHS~~%`$ Wue^_^^% $  >I% $ }V~~$ #1K0x"2"2 FP..w r         ''^?_{twilight ITMP131.TMP templatesheet)et))bTEMPCER38kClarkMicrosoft V1.0{P 8%Euler's formulaS*Z|{This document is an Inspiration 5.0 document. 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