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The quartic equation: alignment with an equivalent tetrahedron

Published online by Cambridge University Press:  23 January 2015

R. W. D. Nickalls
R. W. D. Nickalls*
Affiliation:
5 Elm Bank Drive, Mapperley Park, Nottingham, NG3 5AL, UK, e-mail: dick@nickalls.org
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Extract

The lower polynomials are inextricably linked to the symmetries of polyhedra and Platonic solids [1, 2, 3], and the quartic is no exception; its alter ego is the regular tetrahedron [4]. In this article we present a solution to the problem of aligning the vertices of a tetrahedron with the roots of a particular quartic. After establishing the size of a quartic-equivalent tetrahedron, we derive a triple-angle expression for the alignment rotation, analogous to that for the cubic [5].

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Articles
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The Mathematical Gazette , Volume 96 , Issue 535 , March 2012 , pp. 49 - 55
Copyright
Copyright © The Mathematical Association 2012

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References

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