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The graph M`_k@COOG_G@BB?{?

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

Embedding

An embedding of this graph is given by.

(4, -12, -4)
(12, 0, 12)
(0, 12, -12)
(12, -4, -4)
(12, 6, -6)
(0, 12, 12)
(6, 6, -12)
(12, 12, 12)
(6, 6, 12)
(12, 12, -12)
(6, 12, 6)
(12, 0, -12)
(12, -12, 12)
(12, -12, 0)