[2] She grasped four-dimensional geometry from an early age, and introduced the term "polytope" for a convex solid in four or more dimensions.

[5] She was first exposed to geometric models by her brother-in-law Charles Howard Hinton when she was 17, and developed the ability to visualise four-dimensional space.

[6] She produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods since she had never learned any analytic geometry.

In 1930 she was introduced by her nephew Geoffrey Ingram Taylor to Harold Scott MacDonald Coxeter and they worked together on various problems.

[4] Coxeter later wrote, "The strength and simplicity of her character combined with the diversity of her interests to make her an inspiring friend.

[10] The pioneering spirit of grandfather and mother continued in her son Leonard, who assisted in tuberculosis treatment and invented an artificial pneumothorax apparatus.