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The geodesic is the intersection of the sphere with a plane through its center connecting the two points on its surface – a great circle. ′ → ��′: �� = ∫���� = ∫√��2��′2 + 1���� ⇒ �� = √��2��′2 + 1. (13) �� = ��′�� + ��′′.
A curve whose geodesic curvature is zero everywhere is called a geodesic, and it is (locally) the shortest distance between two points on the surface. Along geodesic curves, the normal vectors to the geodesic coincide with the normal vectors to the surfaces.
You have made a geodesic sphere. You can turn it into a solid (called an “icosahedron”) by gluing colored paper triangles over each of the 20 sides, or you can leave it open and play catch by tossing and catching it with a dowel.
Questions on Geodesic Domes This 3-frequency octahedral geodesic dome is a polyhedron inscribed in a sphere that obtained by subdividing each face of an octahedron into 9 congruent equilateral triangles and projecting outward from the center.
I'm trying to create a very specific geodesic tessellation, but I can't find anything online about it.
It is normal to subdivide the triangles of an icosahedron into triangle patches and project them onto the sphere. However, I noticed an animated GIF on the Wikipedia entry for Geodesic Domes that appears not to follow this scheme. Geodesic spheres generally comprise a mixture of mostly hexagonal triangle patches, with pentagonal patches forming at the vertices of the original icosahedron; in most cases, these pentagons are linked together; that is, following a straight edge from the center of one pentagon leads to the center of another pentagon. In the Wikipedia animation, however, the edge from the center of one pentagon doesn't appear to intersect the center of an adjacent pentagons; instead it intersects the side of the other pentagon.
Where can I go to learn about the math behind this particular geometry? Ideally, I'd like to know of an algorithm for generating such tessellations.
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