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Tetrahedron 4-Compound


Tetrahedron4Compounds

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by angles pi/n for n=2, 3, and 4.

The compounds illustrated above are implemented in the Wolfram Language as PolyhedronData[{"TetrahedronFourCompound", n}] for n=1, ..., 6.

Tetrahedron4CompoundsAndDuals

These tetrahedron 4-compounds are illustrated above together with their duals and common midspheres.

Tetrahedron4CompoundsIntersectionsAndConvexHulls

The common solids and convex hulls are illustrated above.

Tetrahedron4-CompoundNetC3

The net for the hull of the third compound is illustrated above, where for tetrahedra with unit edge lengths,

s_1=1/(144)sqrt(91)
(1)
s_2=2/(9sqrt(7))
(2)
s_3=1/(48)sqrt(19)
(3)
s_4=1/9
(4)
s_5=1/(3sqrt(7))
(5)
s_6=1/5sqrt((13)/7)
(6)
s_7=1/3
(7)
s_8=2/5
(8)
s_9=3/5.
(9)

The hull of this compound has surface area

 S=(1291)/(210sqrt(3)) approx 3.5493.
(10)

See also

Polyhedron Compound, Regular Tetrahedron

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Cite this as:

Weisstein, Eric W. "Tetrahedron 4-Compound." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Tetrahedron4-Compound.html

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