- In
elementary geometry, a
polytope is a
geometric object with flat
sides (faces).
Polytopes are the
generalization of three-dimensional
polyhedra to any...
-
There are six
convex and ten star
regular 4-
polytopes,
giving a
total of sixteen. The
convex regular 4-
polytopes were
first described by the
Swiss mathematician...
- cells. The 4-
polytopes were
discovered by the
Swiss mathematician Ludwig Schläfli
before 1853. The two-dimensional
analogue of a 4-
polytope is a polygon...
-
traditional polytopes (also
called classical or
geometric polytopes) may not be so for
abstract ones, and vice versa. For example, a
traditional polytope is regular...
-
regular 4-
polytopes. The
tesseract is also
called an 8-cell, C8, (regular) octachoron, or
cubic prism. It is the four-dimensional
measure polytope, taken...
-
regular polytopes.
Coxeter lists a few of
these in his book
Regular Polytopes.
McMullen added six in his
paper New
Regular Compounds of 4-
Polytopes. Self-duals:...
-
dimension of the
polytope) — cells,
faces and so on — are also
transitive on the
symmetries of the
polytope, and are
themselves regular polytopes of dimension...
- non-affine
transformations such as
tiling on the
polytopes, and then
converts the
transformed polytopes into equivalent, but
optimized (depending on targeted...
-
regular polytopes in Euclidean,
spherical and
hyperbolic spaces. This
table shows a
summary of
regular polytope counts by rank. Only
counting polytopes of...
-
centers of the 421.
These polytopes are part of a
family of 255 = 28 − 1
convex uniform 8-
polytopes, made of
uniform 7-
polytope facets and
vertex figures...
