- 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...
-
regular polytopes in Euclidean,
spherical and
hyperbolic spaces. This
table shows a
summary of
regular polytope counts by rank. Only
counting polytopes of...
- 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...
- 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...
-
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: 1852:
Ludwig Schläfli
proved in his m****cript
Theorie der
vielfachen Kontinuität that
there are
exactly 6
regular polytopes in 4 dimensions...
-
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...
-
families of
polytopes based on
Cartesian products of lower-dimensional
uniform polytopes. Five are
formed as the
product of a
uniform 4-
polytope with a regular...
- 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...
