- 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 4-
polytopes. The
tesseract is also
called an 8-cell, C8, (regular) octachoron, or
cubic prism. It is the four-dimensional
measure polytope, taken...
- 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 polytopes in Euclidean,
spherical and
hyperbolic spaces. This
table shows a
summary of
regular polytope counts by rank. Only
counting polytopes of...
- image, Coxeter, H.S.M.;
Regular Polytopes, 3rd Edn,
Dover (pbk), 1973, p. 114 Shephard, G.C.; "Regular
complex polytopes", Proc.
London Math. Soc. Series...
-
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...
- as in many
other texts in
discrete geometry,
convex polytopes are
often simply called "
polytopes". Grünbaum
points out that this is
solely to
avoid the...
-
polytopes, and this led to the use of
torsion coefficients. 6-
polytopes may be
classified by
properties like "convexity" and "symmetry". A 6-
polytope...
