- In
elementary geometry, a
polytope is a
geometric object with flat
sides (faces).
Polytopes are the
generalization of three-dimensional
polyhedra to any...
- 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...
-
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...
-
regular polytopes in Euclidean,
spherical and
hyperbolic spaces. This
table shows a
summary of
regular polytope counts by rank. Only
counting polytopes of...
-
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...
- 6-dimensional geometry,
there are 39
uniform polytopes with E6 symmetry. The two
simplest forms are the 221 and 122
polytopes,
composed of 27 and 72
vertices respectively...
- 4-dimensional cross-
polytope also goes by the name
hexadecachoron or 16-cell. It is one of the six
convex regular 4-
polytopes.
These 4-
polytopes were
first described...
-
polytopes, and this led to the use of
torsion coefficients. 6-
polytopes may be
classified by
properties like "convexity" and "symmetry". A 6-
polytope...
-
generalization of the
older category of
semiregular polytopes, but also
includes the
regular polytopes. Further, star
regular faces and
vertex figures (star...
- 5-
polytope is
contained in the 5-
polytope or its interior; otherwise, it is non-convex. Self-intersecting 5-
polytopes are also
known as star
polytopes,...
