The Five Platonic Solids. All the convex 3D Shapes made with all the Same Regular Polygons for Sides, and Same Number at Each Vertex (Corner).
The Tetrahedron.
(Three Triangles Meet at Corners)
Faces=F=4
Vertices=V=4
Edges=E=6
And F + V - E = 2 (Euler's Characteristic)
It is its own Dual because Faces=Vertices=4.
The Cube (Hexahedron).
(Has Faces made of Squares)
Faces=F=6
Vertices=V=8
Edges=E=12
And F + V - E = 2 (Euler's Characteristic)
It is the Dual of the Octahedron, which has 8 faces and 6 corners (vertices).
The Octahedron.
(Four Triangles Meet at Corners)
Faces=F=8
Vertices=V=6
Edges=E=12
And F + V - E = 2 (Euler's Characteristic)
It is the Dual of the Cube (Hexahedron), which has 6 faces and 8 corners (vertices).The Dodecahedron.
(Has Faces made of Pentagons)
Faces=F=12
Vertices=V=20
Edges=E=30
And F + V - E = 2 (Euler's Characteristic)
It is the Dual of the Icosahedron, which has 20 faces and 12 corners (vertices).
The Icosahedron.
(Five Triangles Meet at Corners)
Faces=F=20
Vertices=V=12
Edges=E=30
And F + V - E = 2 (Euler's Characteristic)
It is the Dual of the Dodecahedron, which has 12 faces and 20 corners (vertices).