Divide a Sphere into Many Shapes

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SUMMARY

The discussion focuses on dividing a sphere into multiple geometric shapes, with the initial suggestion being a dodecahedron, which consists of 12 pentagonal faces. For more divisions, the icosahedron, a 20-sided figure with triangular faces, is recommended as a regular solid. If regularity is not a requirement, participants suggest exploring a myriahedron or geodesic domes, which can accommodate a greater number of faces and provide varied geometric configurations.

PREREQUISITES
  • Understanding of geometric solids, specifically dodecahedrons and icosahedrons.
  • Familiarity with the concept of regular and irregular polyhedra.
  • Knowledge of geodesic dome structures and their properties.
  • Basic principles of spherical geometry.
NEXT STEPS
  • Research the properties and applications of the icosahedron in geometry.
  • Explore the concept of myriahedrons and their construction methods.
  • Study geodesic dome design principles and their structural advantages.
  • Investigate advanced geometric shapes and their divisions, such as polyhedral subdivisions.
USEFUL FOR

Mathematicians, architects, and designers interested in geometric shapes and their applications in various fields, including architecture and computational geometry.

frogtag
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Hi a bit random this question, but I'm trying to divide a sphere into many equal shapes (round-ness isn't important). So far I've come up with a dodecahedron, 12 pentagons. This isn't enough of a division for my needs. Can anyone give me the names of geometric shapes that have more divisions please. I found an image of a hexadecagon, but this only showed the divisions for a circle, so I could see the spherical division shape. I hope I've made enough sense for someone to understand what I'm after. It's not homework by the way.

Thanks
 
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It's really hard for me to guess your meaning. You're looking for a shape of some kind, one with many sides, I take it. But I don't know what "divisions for a circle" means, nor "spherical division shape".

If your solid needs to be regular, the only step up from a dodecahedron to a "rounder" figure is an icosahedron, a 20-sided figure with triangles for faces. If you want the individual faces to be as "round" as possible, then a dodecahedron is the best regular solid; the others have triangles or squares as faces.

If you don't need the solid to be regular, you can have as many faces as you want. A myriahedron is possible, if desired...
 

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