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The graph ML?CADG`?gD?Ai@T?

This graph is embeddable. It is even 7-grid embeddable.

Embedding

An embedding of this graph is given by.

(6, -6, 2)
(6, 4, 6)
(0, 6, -4)
(2, 4, 6)
(0, 6, 0)
(6, -6, 0)
(6, 4, -6)
(4, -6, 0)
(6, 0, -6)
(6, 6, 0)
(6, 6, -6)
(6, 0, 0)
(6, 0, 6)
(0, 0, 6)