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The graph M@O?CIAHAC`gCg}??

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

Embedding

An embedding of this graph is given by.

(12, -8, 0)
(12, 0, 0)
(12, -4, 0)
(4, 12, 0)
(0, 12, 0)
(12, -10, -6)
(0, 12, -12)
(8, 12, -4)
(8, 12, 12)
(4, 12, -12)
(0, 12, 12)
(6, 0, 12)
(12, -4, -4)
(0, 0, 12)