Platonic Connections
The following matrix, R , represents the connectivity of a solid where R i , j determines whether there is a connection (edge) between vertices i and j . ("1" indicates a connection or edge, "0" implies no connection).
R = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤
What solid does this represent?
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If you draw it out, you'll see that it is an i c o s a h e d r o n , pictured below.
A big hint is that it has 12 vertices (12 rows and 12 columns) and each vertex connects to 5 other vertices.