Thorold Gosset

Thorold Gosset (1869–1962) was an English lawyer and an amateur mathematician. In mathematics, he is noted for discovering and classifying the semiregular polytopes in dimensions four and higher.

According to H. S. M. Coxeter,^[1] Gosset, after attaining his law degree in 1895 and having no clients, amused himself by attempting to classify the regular polytopes in higher dimensional (greater than three) Euclidean space. After rediscovering all of them, he attempted to classify the "semi-regular polytopes", which he defined as polytopes having regular facets and which are vertex-uniform, as well as the analogous honeycombs, which he regarded as degenerate polytopes. In 1897 he submitted his results to James W. Glaisher, then editor of the journal Messenger of Mathematics. Glaisher was favourably impressed and passed the results on to William Burnside and Alfred Whitehead. Burnside, however, stated in a letter to Glaisher in 1899 that "the author's method, a sort of geometric intuition" did not appeal to him. He admitted that he never found the time to read more than the first half of Gosset's paper. In the end Glashier published only a brief abstract of Gosset results.^[2]

Gosset's results went largely unnoticed for many years. His semiregular polytopes were rediscovered by Elte in 1912^[3] and later by H.S.M. Coxeter who gave both Gosset and Elte due credit.

See also

• Gosset graph

Semiregular figures Gosset enumerated: (his names in parentheses)

• Convex uniform honeycombs, two 3D honeycombs:
  1. Tetrahedral-octahedral honeycomb (Simple tetroctahedric check)
  2. Gyrated alternated cubic honeycomb (Complex tetroctahedric check)
• Uniform polychora, three 4-polytopes:
  1. Rectified 5-cell (Tetroctahedric)
  2. Snub 24-cell (Tetricosahedric)
     • Snub 24-cell honeycomb
  3. Rectified 600-cell (Octicosahedric)
• Semiregular E-polytopes, four polytopes, and one honeycomb:
  1. 5-demicube (5-ic semi-regular), a 5-polytope
  2. 2₂₁ polytope (6-ic semi-regular), a 6-polytope
  3. 3₂₁ polytope (7-ic semi-regular), a 7-polytope
  4. 4₂₁ polytope (8-ic semi-regular), an 8-polytope
  5. 5₂₁ honeycomb (9-ic check) (8D honeycomb)

References

1. ^ Coxeter, H. S. M. (1973). Regular Polytopes ((3rd ed.) ed.). New York: Dover Publications. ISBN 0-486-61480-8.  A brief account of Gosset and his contribution to mathematics is given on page 164.
2. ^ Gosset, Thorold (1900). "On the regular and semi-regular figures in space of n dimensions". Messenger of Mathematics 29: 43–48. 
3. ^ Elte, E. L. (1912). The Semiregular Polytopes of the Hyperspaces. Groningen: University of Groningen. ISBN 141817968X.