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The graph MwE?O_`Aa_?_@F?x?

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

Embedding

An embedding of this graph is given by.

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