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Pentagonal Prism 6-Compound


PentagonalPrism6-Compound

An attractive compound can be constructed of 6 pentagonal prisms having unit edge lengths, as illustrated above.

PentagonalPrism6-CompoundNet

A net for the solid is illustrated above, where

s_1=sqrt((13)/2-(29)/(2sqrt(5)))
(1)
s_2=1/(20)(5-sqrt(5))
(2)
s_3=1/4(3-sqrt(5))
(3)
s_4=sqrt(5)-2
(4)
s_5=1/(10)(5-sqrt(5))
(5)
s_6=1/5(3sqrt(5)-5)
(6)
s_7=1/2(3-sqrt(5)).
(7)

The compound has surface area

 S=3(68-29sqrt(5)+sqrt(1025-458sqrt(5))).
(8)

See also

Pentagonal Prism

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References

Hart, G. "6 Pentagonal Prisms." http://www.georgehart.com/virtual-polyhedra/vrml/compound_of_6_pentagonal_prisms.wrl.

Cite this as:

Weisstein, Eric W. "Pentagonal Prism 6-Compound." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PentagonalPrism6-Compound.html

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