- 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...
-
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...
- 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...
- M. (1947),
Regular Polytopes, Methuen, p. 16 Barnette,
David (1973), "A
proof of the
lower bound conjecture for
convex polytopes",
Pacific Journal of...
- Ziegler, Günter M. (1995). "Chapter 4: Steinitz'
Theorem for 3-
Polytopes".
Lectures on
Polytopes.
Graduate Texts in Mathematics. Vol. 152. Springer-Verlag...
