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The graph M`_[@D?GG_G@AF@w?

This graph is embeddable. It is even 9-grid embeddable.

Embedding

An embedding of this graph is given by.

(2, 8, -8)
(8, 0, 2)
(4, -8, -4)
(0, -4, 8)
(8, -2, 0)
(2, 8, 4)
(0, 8, 8)
(8, 8, -8)
(2, -4, -8)
(8, 4, 0)
(8, 0, 0)
(0, 8, 0)
(0, 0, 8)
(8, -4, 4)