page_title: Convex uniform honeycomb
hierarchical_section_title: Convex uniform honeycomb
context_page_description: In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.
  Twenty-eight such honeycombs are known:
  the familiar cubic honeycomb and 7 truncations thereof;
  the alternated cubic honeycomb and 4 truncations thereof;
  10 prismatic forms based on the uniform plane tilings;
  5 modifications of some of the above by elongation and/or gyration.
  They can be considered the three-dimensional analogue to the uniform tilings of the plane.
  The Voronoi diagram of any lattice forms a convex uniform honeycomb in which the cells are zonohedra.
context_section_description: In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.
  Twenty-eight such honeycombs are known:
  the familiar cubic honeycomb and 7 truncations thereof;
  the alternated cubic honeycomb and 4 truncations thereof;
  10 prismatic forms based on the uniform plane tilings (11 if including the cubic honeycomb);
  5 modifications of some of the above by elongation and/or gyration.
  They can be considered the three-dimensional analogue to the uniform tilings of the plane.
  The Voronoi diagram of any lattice forms a convex uniform honeycomb in which the cells are zonohedra.
caption: The alternated cubic honeycomb is one of 28 space-filling uniform tessellations in Euclidean 3-space, composed of alternating yellow tetrahedra and red octahedra.
exif: {}