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The graph M`@K@?QE@AW?AF@w?

This graph is embeddable. It is even 13-grid embeddable.

Embedding

An embedding of this graph is given by.

(0, 12, -12)
(0, 12, 12)
(12, 0, 12)
(8, -12, -8)
(8, -12, 0)
(12, 8, -8)
(6, -12, -12)
(12, 0, -12)
(12, 12, -6)
(12, 8, 0)
(0, 12, 0)
(12, 0, 0)
(0, 0, 12)
(12, -6, 12)