Extrusion (InstanceTopic, 3)
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'''Extrusion''' is the simplest operation which creates an ''n''+1-dimensional shape from an ''n''-dimensional shape. Extruding a shape causes a [[hyperprism]] to be formed, of which the base is the original shape. The length of the new prism can be specified as an argument to the extrusion operation. If unspecified, a common default is to use the length of the largest [[cardinal]] side. | '''Extrusion''' is the simplest operation which creates an ''n''+1-dimensional shape from an ''n''-dimensional shape. Extruding a shape causes a [[hyperprism]] to be formed, of which the base is the original shape. The length of the new prism can be specified as an argument to the extrusion operation. If unspecified, a common default is to use the length of the largest [[cardinal]] side. | ||
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| + | After the extrusion, the number of elements change similarly to going down a row in [[wikipedia:Pascal's triangle|Pascal's triangle]]. Each count is doubled and then increased by the count one dimension below it (and a single cell of the shape's dimension is formed). For example, when extruding the cube (which has 8 vertices, 12 edges, 6 faces and of course 1 cell), a tesseract is formed, which will have 8*2 = 16 vertices, 12*2+8 = 32 edges, 6*2+12 = 24 faces, 1*2+6 cells and a single new teron. | ||
[[Category:Geometric operations]] | [[Category:Geometric operations]] | ||
Revision as of 23:25, 11 November 2008
Extrusion is the simplest operation which creates an n+1-dimensional shape from an n-dimensional shape. Extruding a shape causes a hyperprism to be formed, of which the base is the original shape. The length of the new prism can be specified as an argument to the extrusion operation. If unspecified, a common default is to use the length of the largest cardinal side.
After the extrusion, the number of elements change similarly to going down a row in Pascal's triangle. Each count is doubled and then increased by the count one dimension below it (and a single cell of the shape's dimension is formed). For example, when extruding the cube (which has 8 vertices, 12 edges, 6 faces and of course 1 cell), a tesseract is formed, which will have 8*2 = 16 vertices, 12*2+8 = 32 edges, 6*2+12 = 24 faces, 1*2+6 cells and a single new teron.
