- In geometry, a
parallelohedron is a
polyhedron that can be
translated without rotations in 3-dimensional
Euclidean space to fill
space with a honeycomb...
- to the
short diagonals of the rhombi. The
rhombic dodecahedron is a
parallelohedron, a space-filling polyhedron, dodecahedrille,
being the dual 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...
- the
hexagonal prism,
which classifies as an
irregular octahedron and
parallelohedron, is able to
tessellate space as a three-dimensional
analogue of the...
-
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)...
-
tessellate 3-dimensional
space and is
called a
primary parallelohedron. Each
primary parallelohedron is
combinatorially equivalent to one of five types:...
- four-sided
parallelogon is
called a parallelogram. The
faces of a
parallelohedron (the
three dimensional analogue) are
called parallelogons. Quadrilateral...
- dimensions,
hexagonal prisms with
parallel opposite faces are
called parallelohedrons and
these can
tessellate 3-space by translation. In
addition to the...
-
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...
