Classifying 3D Shapes into Finite Categories

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SUMMARY

The classification of 3D shapes into a finite number of categories is inherently complex due to the infinite possibilities of shape construction. A practical approach involves classifying shapes based on their vertices and the number of planes used in their construction. For example, a cube and a rectangular prism can be represented as figures with eight 3-plane vertices, denoted as 8*(90, 90, 90) to indicate the angles of the planes. However, the arrangement of vertices in 3D space adds further complexity to this classification system.

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  • Understanding of 3D geometry concepts
  • Familiarity with vertices and planes in spatial structures
  • Knowledge of mathematical notation for geometric representation
  • Basic skills in spatial reasoning and visualization
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Mathematicians, educators, 3D modelers, and anyone interested in the classification and representation of geometric shapes in three-dimensional space.

Aeneas
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Please can someone tell me whether anyone has managed to classify all possible 3-D shapes into a finite and usefully small number of categories? At school level, most shapes seem to be some part, or combination, of:
 
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There are too many impracticalities with what you are trying to do. 3d shapes can be made infinitely complex. You can classify vertices though, using the number of planes that are used construct them as your reference. A cube and rectangular prism alike could then be represented as figures consisting of eight 3-planes vertices, with say the notation 8*(90, 90, 90) to specify the angles that each of the planes represent. Of course, it's not as simple as that when it comes to complicated shapes - the different possible arrangements of the vertices in 3d space have to be taken into account.
 
Last edited:
Many thanks, Werg22.
 

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