page_title: Abstract polytope
section_title: Hosohedra and hosotopes
hierarchical_section_title: Abstract polytope / Examples of higher rank / Hosohedra and hosotopes
context_page_description: In mathematics, an abstract polytope is an algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope without specifying purely geometric properties such as angles or edge lengths. A polytope is a generalisation of polygons and polyhedra into any number of dimensions.
  An ordinary geometric polytope is said to be a realization in some real N-dimensional space, typically Euclidean, of the corresponding abstract polytope. The abstract definition allows some more general combinatorial structures than traditional definitions of a polytope, thus allowing many new objects that have no counterpart in traditional theory.
context_section_description: The digon is generalized by the hosohedron and higher dimensional hosotopes, which can all be realized as spherical polyhedra – they tessellate the sphere.
caption: A hexagonal hosohedron, realized as a spherical polyhedron.