New Regular Compounds of 4-Polytopes

  • Peter McMullenEmail author
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 27)


This note describes six apparently new regular compounds of polytopes in \(\mathbb {E}^4\), that were missed by Coxeter in his systematic faceting procedure. In fact, three have the same symbols as ones in Coxeter’s list (and two are nearly the same); however, their symmetry groups are much smaller. The treatment relies heavily on the use of quaternions.


Regular polytope Compound Quaternion 

MSC (2010)

Primary 51M20 Secondary 52B15 


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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University College LondonLondonEngland

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