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Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres) In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point.
Geodesic polyhedra are constructed by subdividing faces of simpler polyhedra, and then projecting the new vertices onto the surface of a sphere. A geodesic polyhedron has straight edges and flat faces that approximate a sphere, but it can also be made as a spherical polyhedron (a tessellation on a sphere ) with true geodesic curved edges on the ...
A portion of the curve x = 2 + cos(z) rotated around the z-axis A torus as a square revolved around an axis parallel to one of its diagonals.. A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints). [1]
Dyson Sphere Program takes place in a futuristic science fiction world, where a society exists primarily in a virtual computer space, which demands a great deal of power and computational ability. To expand that, they have sent one of their members, the player, into the real universe to construct a Dyson sphere from resources in a nearby star ...
A clockwise and counterclockwise whirl generator, w w = wrw generates GP(7,0) in class 1. In general, a whirl can transform a GP( a , b ) into GP( a + 3 b ,2 ab ) for a > b and the same chiral direction.
The March 1, 1943, edition of Life magazine included a photographic essay titled "Life Presents R. Buckminster Fuller's Dymaxion World", illustrating a projection onto a cuboctahedron, including several examples of possible arrangements of the square and triangular pieces, and a pull-out section of one-sided magazine pages with the map faces printed on them, intended to be cut out and glued to ...
In mathematics, a unit sphere is a sphere of unit radius: the set of points at Euclidean distance 1 from some center point in three-dimensional space. More generally, the unit n {\displaystyle n} -sphere is an n {\displaystyle n} -sphere of unit radius in ( n + 1 ) {\displaystyle (n+1)} - dimensional Euclidean space ; the unit circle is a ...