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Master Tetrahedron
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A Master Skewb transformed into tetrahedral shape.

This is the master variant of the HMT aka Halper-Meier-Tetrahedron. The HMT can be made out of a skewb and this Master Tetrahedron was built out of Master Skewb. It is a result of the special properties of corner-turning hexahedrons that this puzzle does not change shape while scrambled. Other hexahedron->tetrahedron-transformations (e.g. Pyramorphix) do this.
In 2013 Traiphum Prungtaengkit presented the pillowed version in image #6.

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Thank you to the following people for their assistance in helping collect the information on this page: Andreas Nortmann.

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