Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
What types of multi-dimensional shapes are there?
I am interested in basics of multi-dimensional geometry.
Simplexes are made by adding an extra dot or vertex for each dimension. I like to think of these as triangular shapes.
Other shapes that have multi-D versions are Square or cubic shapes such as hyper-cubes that are made by duplicating or sliding the shape into the next dimension; and circular.spherical shapes, where every point is equidistant from a center origin, or made by spinning into the next dimension.
What other types of multi-Dimensional shape series exist?
3 Answers
- mathematicianLv 71 decade agoFavorite Answer
I assume that you want shapes with a lot of symmtery, otherwise there would be too many to name.
It is also possible to find higher dimensional analogs of octahedra. This goes as follows: For two dimensions, you have a square. For three, put points above and below the square and draw lines to each vertex of the square. This gives an ocahedron. For four dimensions, put points 'above' and 'below' the octahedron and draw lines to each vertex of the octahedron. This can continue to any number of dimensions.
The other generalizations of polygons are limited to low dimensions. There are only 5 Platonic solids, only three of which go to every dimension (simplex, cube, octahedron). The other two (dodecahedron and isosahedron) can be generalized to some extent, but not to all dimensions. Look up the concept of a 'polytope'.
- 1 decade ago
I am a Designer of machine tools and tooling's to make automobile components!
You are looking for 3 dimensional geometries which are basically two types!
3D solids with flat faces and 3D solid with spherical /curved faces.
Cube is a very good example to 3D solids with flat faces!
A tetrahedron(four equal faced) is another solid of this category which is a bit difficult to imagine!Your words "I like to think of these as triangular shapes" hints at why you have raised your question! This type of solids is difficult to imagine. However you can imagine these easily in relation to a cube! Said figure based explanation has been given in an article "Vedic matrix-0" which you can read on site <www.vedicmatrx.org>. (You may have to carefully read the article but you will grasp matters from concerned figures. Relation of cube and tetrahedron is clearly shown it. Further how to create more 'related flat faced solids' is also given in article. It will give you a very good idea relating your need.
Your question relate multi-dimensional shapes which I regard combination of flat faced and curve-set solids
flat faced solids are created by "extrusion" and curve-set solid by revolving a curved area about an axis! A usual "Auto Cad" 3D will teach you that!
Combination solids indicated by you is a vast possibility, which I recommend you to learn slowly after grasping concerned 3D creation basics!
Infinite possibilities to imagine and create 3D models exists and I do not want to confuse you by explaining an axample of it!
Regards!
