- In geometry, a
polyhedron (pl.:
polyhedra or polyhedrons; from Gr**** πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure...
- the same
number of
faces meet at each vertex.
There are only five such
polyhedra:
Geometers have
studied the
Platonic solids for
thousands of years. They...
- of
selected geodesic polyhedra and
Goldberg polyhedra, two
infinite classes of
polyhedra.
Geodesic polyhedra and
Goldberg polyhedra are
duals of each other...
-
uniform polyhedra with
degenerate vertex figures which have
overlapping edges (not
counted by Coxeter); The
uniform tilings (infinite
polyhedra) 11 Euclidean...
-
convex regular polyhedra (the
Platonic solids), and four
regular star
polyhedra (the Kepler–Poinsot
polyhedra),
making nine
regular polyhedra in all. In addition...
- In geometry, a Kepler–Poinsot
polyhedron is any of four
regular star
polyhedra. They may be
obtained by
stellating the
regular convex dodecahedron and...
-
authors exclude uniform polyhedra (in
which all
vertices are
symmetric to each other) from the definition;
uniform polyhedra include Platonic and Archimedean...
-
figures remain combinatorial or
abstract polyhedra, but not all can also be
constructed as
geometric polyhedra.
Starting with any
given polyhedron, the...
- of the
uniform polyhedra are also star
polyhedra.
There are two
infinite classes of
uniform polyhedra,
together with 75
other polyhedra. They are 2 infinite...
- lower-case
letter chi). The
Euler characteristic was
originally defined for
polyhedra and used to
prove various theorems about them,
including the classification...
