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February 1st, 2017, 10:00 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory  Volume/(Surface area * edge * number of corners)
Does this quantity differ only +/ 10% for Platonic solids? How about for other groups of solids?

February 2nd, 2017, 12:04 PM  #2 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory 
For a tetrahedron, volume=(2^.5/12)a^3, surface area=(3^.5)a^2, edge=a, corners=4 For a cube, volume =a^3, surface area=6a^2, edge=a, corners=8 For an octahedron, volume=(2^.5/3)a^3, surface area=2(3^.5)a^2, edge=a, corners=6 For a dodecahedron, volume=(7.663...)a^3, surface area=(20.646...)a^2, edge=a, corners=20 For an icosahedron, volume=(2.182...)a^3, surface area=(8.660...)a^2, edge=a, corners=12 volume/(surface area * edge * number of corners)=? Last edited by Loren; February 2nd, 2017 at 12:11 PM. 
February 4th, 2017, 04:08 PM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory  volume/(surface area * edge * number of corners)=P For a tetrahedron_____.01701...=P For a cube_____.02083...=P For an octahedron_____.02268...=P For a dodecahedron_____.01856...=P For an icosahedron_____.02100...=P Can you explain this cluster of values given P for Platonic solid geometries? 

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area, corners, edge, number, volume or surface 
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