Hypertope

A hypertope is a certain generalization of an abstract polytope, where elements are no longer linearly ordered by their rank.

Definition

A hypertope is a thin residually connected incidence geometry.

Relationship to abstract polytopes

Typically a abstract polytope is converted to a hypertope by considering all proper elements of the polytope, with the type function being the rank of each element. This gives a hypertope for every polytope, however the nullitope gives a hypertope of rank 0, rather than of rank -1. It is impossible for a hypertope to have a rank less than zero, so the nullitope is not usually considered a hypertope.

Only proper elements are considered because if all elements of an abstract polytope are considered the resulting incidence geometry is not thin.

Bibliography

• Fernandes, Maria (2014). "Regular and chiral hypertopes" (PDF).