NCTM embraces Synergetics

The National Council of Teachers of Mathematics has officially blessed a lesson plan featuring the tetrahedron in a non-traditional role: as a unit of volume. An octet truss is built, called a kite, an allusion to Alexander Graham Bell.
The Synergetics Folio demonstration, that a regular octahedron has four times the volume of a regular tetrahedron of the same edge, is described in detail. Students are led to the right conclusions about how linear, areal and volumetric quantities relate, as 1st, 2nd and 3rd power phenomena. After a 2-frequency tetrahedron is built, students are encouraged to increase the frequency even more.

http://illuminations.nctm.org/LessonDetail.aspx?ID=L639

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Tetrahedral Kites

Each student constructs a tetrahedron and describes the linear, area and volume using non‑traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed.

Images below by David Koski using vZome by Scott Vorthmann.