- 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...
- of many
classes of polyhedra:
Platonic solid,
regular polyhedron,
parallelohedron, zonohedron, and plesiohedron. The dual
polyhedron of a cube is the...
- three-dimensional
primary parallelohedrons, one of
which is the
truncated octahedron. More generally,
every permutohedron and
parallelohedron is zonohedron, a...
- 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...
-
tessellate 3-dimensional
space and is
called a
primary parallelohedron. Each
primary parallelohedron is
combinatorially equivalent to one of five types:...
-
Rhombohedron Type
prism Faces 6
rhombi Edges 12
Vertices 8
Symmetry group Ci , [2+,2+], (×),
order 2
Properties convex, equilateral, zonohedron,
parallelohedron...
- domain.
Further contributions were made from
Evgraf Fedorov, (Fedorov
parallelohedron),
Georgy Voronoy (Voronoi polyhedron), and Paul
Niggli (Wirkungsbereich)...
-
different geometry than the face-transitive
rhombic dodecahedron. It is a
parallelohedron. This
shape appears in a 1752 book by John
Lodge Cowley,
labeled as...
- four-sided
parallelogon is
called a parallelogram. The
faces of a
parallelohedron (the
three dimensional analogue) are
called parallelogons. Quadrilateral...
