Definition & Meaning | English word SPACE-FILLING

Definitions of SPACE-FILLING

1. (geometry) That fills a closed (typically 2-dimensional or 3-dimensional) space.

Examples of Using SPACE-FILLING in a Sentence

• It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension.
• In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or more generally an n-dimensional unit hypercube).
• In the continuity of early 20th century examples of space-filling curves—the Koch-Peano curve, Cesàro and Lévy C curve, all special cases of the general de Rham curve—and following the path of Benoit Mandelbrot, Gosper discovered the Peano-Gosper curve, before engaging with variations on the Harter-Heighway dragon.
• Most of the following definitions of a vertex figure apply equally well to infinite tilings or, by extension, to space-filling tessellation with polytope cells and other higher-dimensional polytopes.
• The square orthobicupola forms space-filling honeycombs with tetrahedra; with cubes and cuboctahedra; with tetrahedra and cubes; with square pyramids, tetrahedra and various combinations of cubes, elongated square pyramids and/or elongated square bipyramids.
• Aether theories, proposing space-filling substance that propagates electromagnetic or gravitational forces.
• The gyrobifastigium is one of five convex polyhedra with regular faces capable of space-filling (the others being the cube, truncated octahedron, triangular prism, and hexagonal prism) and it is the only Johnson solid capable of doing so.
• The elongated triangular orthobicupola forms space-filling honeycombs with tetrahedra and square pyramids.
• The elongated triangular gyrobicupola forms space-filling honeycombs with tetrahedra and square pyramids.
• Along with the rhombic 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.
• A space-filling tessellation, the trapezo-rhombic dodecahedral honeycomb, can be made by translated copies of this cell.
• The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells.
• The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space.
• The bitruncated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of truncated octahedra (or, equivalently, bitruncated cubes).
• In hyperbolic geometry, the order-4 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) of hyperbolic 3-space.
• The quarter cubic honeycomb, quarter cubic cellulation or bitruncated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space.
• The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of identical tetragonal disphenoidal cells.
• In hyperbolic geometry, the order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.
• In hyperbolic geometry, the order-5 cubic honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.
• In geometry, the icosahedral honeycomb is one of four compact, regular, space-filling tessellations (or honeycombs) in hyperbolic 3-space.
• The Gosper curve, named after Bill Gosper, also known as the Peano-Gosper Curve and the flowsnake (a spoonerism of snowflake), is a space-filling curve whose limit set is rep-7.
• The "helical hyperspatial code", or HHCode, as developed by CHS and implemented by Oracle Spatial, comprises a form of space-filling curve.
• Space-filling calotte models are also referred to as CPK models after the chemists Robert Corey, Linus Pauling, and Walter Koltun, who over a span of time developed the modeling concept into a useful form.
• In geometry, he enumerated and published a list of 25 convex uniform honeycombs in 1905 (the space-filling tessellations of regular and semiregular polyhedra).
• The trihexagonal prismatic honeycomb or trihexagonal prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space.

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