- In geometry, a
parallelohedron is a
polyhedron that can be
translated without rotations in 3-dimensional
Euclidean space to fill
space with a honeycomb...
-
Catalan solid, it is the dual
polyhedron of the cuboctahedron. As a
parallelohedron, the
rhombic dodecahedron can be used to
tesselate its
copies in space...
-
Voronoi cell of a
symmetric Delone set. The
plesiohedra include the
parallelohedrons,
which can be
translated without rotating to fill a space—called honeycomb—in...
- three-dimensional
primary parallelohedrons, one of
which is the
truncated octahedron. More generally,
every permutohedron and
parallelohedron is zonohedron, a...
- dimensions,
hexagonal prisms with
parallel opposite faces are
called parallelohedrons and
these can
tessellate 3-space by translation. In
addition to the...
- dodecahedron, it is a space-filling polyhedron, one of the five
types of
parallelohedron identified by
Evgraf Fedorov that tile
space face-to-face by translations...
-
Rhombohedron Type
prism Faces 6
rhombi Edges 12
Vertices 8
Symmetry group Ci , [2+,2+], (×),
order 2
Properties convex, equilateral, zonohedron,
parallelohedron...
-
tessellate 3-dimensional
space and is
called a
primary parallelohedron. Each
primary parallelohedron is
combinatorially equivalent to one of five types:...
- domain.
Further contributions were made from
Evgraf Fedorov, (Fedorov
parallelohedron),
Georgy Voronoy (Voronoi polyhedron), and Paul
Niggli (Wirkungsbereich)...
-
group D3, [2,3]+, (223),
order 6 Dual
polyhedron trigonal antiprism Properties convex,
equilateral polygon, face-transitive, zonohedron,
parallelohedron...
