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The graph MHdE?I?G?H`I?pCI_

This graph is embeddable. It is even 5-grid embeddable.

Embedding

An embedding of this graph is given by.

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