expansionɪkˈspæn ʃən
expansion (n)
- plural
- expansions
expansion
English Definitions:
expansion, enlargement (noun)
the act of increasing (something) in size or volume or quantity or scope
expansion (noun)
a function expressed as a sum or product of terms
"the expansion of (a+b)^2 is a^2 + 2ab + b^2"
expansion, enlargement, elaboration (noun)
a discussion that provides additional information
expansion, expanding upon (noun)
adding information or detail
expansion (Noun)
The act or process of expanding.
expansion (Noun)
The fractional change in unit length per unit length per unit temperature change.
expansion (Noun)
A new addition.
expansion (Noun)
A product to be used with a previous product.
Expansion
In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements. Equivalently this operation can be imagined by keeping facets in the same position but reducing their size. According to Coxeter, this multidimensional term was defined by Alicia Boole Stott for creating new polytopes, specifically starting from regular polytopes to construct new uniform polytopes. The expansion operation is symmetric with respect to a regular polytope and its dual. The resulting figure contains the facets of both the regular and its dual, along with various prismatic facets filling the gaps created between intermediate dimensional elements. It has somewhat different meanings by dimension. In a Wythoff construction, an expansion is generated by reflections from the first and last mirrors. By dimension: ⁕A regular {p} polygon expands into a regular 2n-gon. ⁕The operation is identical to truncation for polygons, t0,1{p} and has Coxeter-Dynkin diagram . ⁕A regular {p,q} polyhedron expands into a polyhedron with vertex figure p.4.q.4. ⁕This operation for polyhedra is also called cantellation, t0,2{p,q}, and has Coxeter-Dynkin diagram .For example, a rhombicuboctahedron can be called an expanded cube, expanded octahedron, as well as a cantellated cube or cantellated octahedron.
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"expansion." Kamus.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.kamus.net/english/expansion>.
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