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March 23rd, 2017, 10:13 PM   #1
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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.
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March 24th, 2017, 05:48 PM   #2
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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

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March 24th, 2017, 06:44 PM   #3
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Originally Posted by agentredlum View Post
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?
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March 24th, 2017, 09:19 PM   #4
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That's true except the cube
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March 25th, 2017, 02:28 PM   #5
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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?
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March 26th, 2017, 11:16 AM   #6
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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
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March 26th, 2017, 12:34 PM   #7
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At least, can you see the symmetry?
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