March 23rd, 2017, 09:13 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 363 Thanks: 26 Math Focus: Number theory  Unique Platonic solids' part
For the five Platonic solids (regular polyhedra), find which number among all their corners, edges and faces is unique.

March 24th, 2017, 04:48 PM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 
The Tetrahedron , Cube and Dodecahedron have 3 edges at every corner so corners is out The Cube and the Octahedron have 12 edges each so edges is out Must be the number of faces Tetrahedron has 4 faces Cube has 6 faces Octahedron has 8 faces Dodecahedron has 12 faces Eicosahedron has 20 faces 
March 24th, 2017, 05:44 PM  #3  
Senior Member Joined: Sep 2015 From: USA Posts: 1,980 Thanks: 1027  Quote:
 
March 24th, 2017, 08:19 PM  #4 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 
That's true except the cube 
March 25th, 2017, 01:28 PM  #5 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 363 Thanks: 26 Math Focus: Number theory 
Each of the five Platonic solids (convex, regular polyhedra) includes its components  corners, edges and faces. Of these total 15 categories, which has an unduplicated total overall?

March 26th, 2017, 10:16 AM  #6 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 363 Thanks: 26 Math Focus: Number theory 
ARRG! I feel slightly like Euler with my farsightedness! I withdraw my initial hypothesis. Corners___edges______ faces 4__________6__________4 8__________12_________6 6__________12_________8 20_________30_________12 12_________30_________20 
March 26th, 2017, 11:34 AM  #7 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 363 Thanks: 26 Math Focus: Number theory 
At least, can you see the symmetry?


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