She found that there were exactly six regular polytopes on four dimensions and that they are bounded by 5, 16 or 600 tetrahedra, 8 cubes, 24 octahedra or 120 dodecahedra. She then produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods for the simple reason that she had never learned any analytic geometry. She made beautiful cardboard models of all these sections.
Read The Princess of Polytopia: Alicia Boole Stott and the 120-cell, by Tony Phillips of Stony Brook University, free from the American Mathematical Society, After taking up secretarial work near Liverpool in 1889 she met and married Walter Stott in 1890. Stott learned of Pieter Schoute's work on central sections of the regular polytopes in 1895 and Alicia Stott sent him photographs of her cardboard models. Schoute came to England and worked with Alicia Stott, persuading her to publish her results which she did in two papers published in Amsterdam in 1900 and 1910.
The University of Groningen honoured her by inviting her to attend the tercentenary celebrations of the university and awarding her an honorary doctorate in 1914.
In 1930 she was introduced to Coxeter and they worked together on various problems. Alicia Stott made two further important discoveries relating to constructions for polyhedra related to the golden section. Coxeter described his time doing joint work with her saying:
"The strength and simplicity of her character combined with the diversity of her interests to make her an inspiring friend."
Her nephew was the fluid dynamicist, Geoffrey Ingram Taylor.