# Category: Space-filling polyhedra

Elongated gyrobifastigium
In geometry, the elongated gyrobifastigium or gabled rhombohedron is a space-filling octahedron with 4 rectangles and 4 right-angled pentagonal faces.
Cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges a
Triangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangul
Hill tetrahedron
In geometry, the Hill tetrahedra are a family of space-filling tetrahedra. They were discovered in 1896 by M. J. M. Hill, a professor of mathematics at the University College London, who showed that t
Parallelohedron
In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb in which all copies of the polyhedron meet face-
Trapezo-rhombic dodecahedron
In geometry, the trapezo-rhombic dodecahedron or rhombo-trapezoidal dodecahedron is a convex dodecahedron with 6 rhombic and 6 trapezoidal faces. It has D3h symmetry. A concave form can be constructed
Truncated octahedron
In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14
Honeycomb (geometry)
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellat
First stellation of the rhombic dodecahedron
In geometry, the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon.It is a stellation of the rhombic dodecahedron and
Trigonal trapezohedron
In geometry, a trigonal trapezohedron is a rhombohedron (a polyhedron with six rhombus-shaped faces) in which, additionally, all six faces are congruent. Alternative names for the same shape are the t
Rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cubocta
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five
Rhombohedron
In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a three-dimensional figure with six faces which are rhombi. It is a special case of a parallelepiped wher
Orthobifastigium
In geometry, the orthobifastigium (digonal orthobicupola), is formed by gluing together two triangular prisms on their square faces, but without twisting. With regular faces, it has coplanar faces, so
Parallelepiped
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as
Hexagonal prism
In geometry, the hexagonal prism is a prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 faces, 18 edges, and 12 vertices. Since it has 8 faces, it is an octahedron. However, the
Ten-of-diamonds decahedron
In geometry, the ten-of-diamonds decahedron is a space-filling polyhedron with 10 faces, 2 opposite rhombi with orthogonal major axes, connected by 8 identical isosceles triangle faces. Although it is
Plesiohedron
In geometry, a plesiohedron is a special kind of space-filling polyhedron, defined as the Voronoi cell of a symmetric Delone set.Three-dimensional Euclidean space can be completely filled by copies of
Space-filling polyhedron
In geometry, a space-filling polyhedron is a polyhedron that can be used to fill all of three-dimensional space via translations, rotations and/or reflections, where filling means that, taken together
Stereohedron
In geometry and crystallography, a stereohedron is a convex polyhedron that fills space isohedrally, meaning that the symmetries of the tiling take any copy of the stereohedron to any other copy. Two-
Triakis truncated tetrahedron
In geometry, the triakis truncated tetrahedron is a convex polyhedron made from 4 hexagons and 12 isosceles triangles. It can be used to tessellate three-dimensional space, making the triakis truncate
Elongated dodecahedron
In geometry, the elongated dodecahedron, extended rhombic dodecahedron, rhombo-hexagonal dodecahedron or hexarhombic dodecahedron is a convex dodecahedron with 8 rhombic and 4 hexagonal faces. The hex
Gyrobifastigium
In geometry, the gyrobifastigium is the 26th Johnson solid (J26). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one pri