simplicial
- adjective
- /sɪmˈplɪʃəl/
- Specialized
:
simplicial
- The architect designed the new pavilion with simplicial components, ensuring a strong yet elegant framework.
- simplicial subdivision
- simplicial sector
- regular simplicial
Examples
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The facets of a simplicial sector in Rn, n > 3 do not have, in general, consistent boundary behavior, which further implies that switching upon hitting a boundary in higher dimensional spaces may give rise to separate trajectory bundles moving to different regions.
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However, nearly uniform simplicial subdivisions of the unit n-sphere with corresponding refinable ray partitions can be generated.
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All points generated on the boundary are subsequently pulled up to the unit n-sphere, forming a nearly regular simplicial subdivision.
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In Rn, it is natural for the switching boundaries to be the facets lying on the intersection of adjacent simplicial sectors.
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And diagrams like these have been able to, we've been able to map them onto the simplicial complexes that exist in these subgraphs.
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Any conic subdivision on the plane is simplicial; therefore, each conic sector has exactly two boundaries (rays) and adjacent sectors.
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This special property is lost in Rn, n > 3, where each simplicial sector has exactly n + 1 vertices (n if the origin is excluded), n facets, and neighboring sectors.
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Moreover, regular polygons induce ray partitions where the angles between consecutive rays are equal, and there is a regular simplicial decomposition in equilateral triangles.
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The artist created a beautiful model using simplicial shapes to represent the complex structure of the ancient temple.
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In mathematics, a simplicial complex can be constructed from triangles to simplify the analysis of multidimensional spaces.
Synonyms
6
4.1
Relating to simple shapes like lines and circles used in design
1
6.1
A shape that has straight flat sides like a triangle or square
How Simplicial
- Specialized
- Specialized
1
7.9
Surface Forms
Morphology
simplicial = simplex (semi-transparent) = simplic + ial
Formally derived from the technical term 'simplex' with the adjectival suffix '-ial', but the stem shape ('simplic-') and the specialized mathematical sense make it less obvious to general learners.
Etymology
Simplicial comes from the Latin word simplex, which means 'simple' or 'single' and shares the same root as the everyday word simple. In mathematics a simplex is a very basic shape such as a triangle in two dimensions or a small pyramid in three dimensions, so simplicial means 'made of these simple shapes' and is used for objects built from triangles or their higher-dimensional versions.