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The graph L`_SQH_?@o_U@T

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

Embedding

An embedding of this graph is given by.

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