- 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...
-
convex regular polyhedra (the
Platonic solids), and four
regular star
polyhedra (the Kepler–Poinsot
polyhedra),
making nine
regular polyhedra in all. In addition...
-
figures remain combinatorial or
abstract polyhedra, but not all can also be
constructed as
geometric polyhedra.
Starting with any
given polyhedron, the...
-
uniform polyhedra with
degenerate vertex figures which have
overlapping edges (not
counted by Coxeter); The
uniform tilings (infinite
polyhedra) 11 Euclidean...
- 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...
- five
convex regular polyhedra are
called the
Platonic solids. The
vertex figure is
given with each
vertex count. All
these polyhedra have an
Euler characteristic...
- lower-case
letter chi). The
Euler characteristic was
originally defined for
polyhedra and used to
prove various theorems about them,
including the classification...
-
polygons whose vertices are not all in the same plane, and
extended it to
polyhedra.
While apeirohedra are
typically required to tile the 2-dimensional plane...
