polytope

It is the final figure in the 1 polytope family.

More recently, the concept of a polytope has been further generalized.

It is possible that the Universe itself has the form of some higher polytope, regular or otherwise.

This polytope is one of 135 uniform 8-polytopes with A symmetry.

It is also the skeleton of an abstract regular polytope, the 57-cell.

A polytope in eight dimensions is called a 8-polytope.

An Cubic honeycomb is not a polytope in the traditional sense.

The 1-skeleton of the 3 polytope is called a Gosset graph.

In 7-dimensional geometry, 2 is a uniform polytope, constructed from the E7 group.

The 4 polytope is last in a family called the k polytopes.

It can also be called an enneazetton, or ennea-8-tope, as a 9-facetted polytope in 8-dimensions.

To define an abstract polytope, a few preliminary concepts are needed.

The faces of a uniform polytope must be regular.

Each uniform polytope in the sequence is the vertex figure of the next.

The monostatic polytope in 3-space they constructed has only 19 faces, the record so far.

We shall present a precise, formal definition of an abstract polytope below.

They are centered at the positions of the 240 vertices in the 4 polytope.

This polytope is the vertex figure for the 1 honeycomb.

In rigorous treatments, a triangle is therefore called a 2-simplex (see also Polytope).

The vertices of the polytope are also called basic feasible solutions.

Questions about polytope diameter are of independent mathematical interest.

A polytope is said to be pointed if it contains at least one vertex.

An example of a non-pointed polytope is the set .

At the start of the 20th century, the definition of a regular polytope was as follows.

More generally, every Hanner polytope has exactly 3 faces.