My Math Forum Unique Platonic solids' part

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 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 Thanks from Loren
March 24th, 2017, 05:44 PM   #3
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 Originally Posted by agentredlum 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
aren't they named for the number of faces they have?

 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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