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The graph M@@?_PC_pBP?B`{@?

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

Embedding

An embedding of this graph is given by.

(0, 12, 0)
(12, -12, 0)
(4, -12, 0)
(12, 4, 0)
(0, 12, 12)
(12, 12, 12)
(4, -12, -12)
(4, 12, -12)
(6, 6, -12)
(12, 0, 4)
(12, 4, 8)
(12, 0, 0)
(0, 12, -12)
(0, 0, 12)