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The pattern can be extended outward in concentric hexagonal rings of circles, as shown. The first row shows rings of circles. The second row shows a three-dimensional interpretation of a set of n×n×n cube of spheres viewed from a diagonal axis. The third row shows the pattern completed with partial circle arcs within a set of completed circles.
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In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
The popularity of the Cube is reflected in its strong sales—in 2022, 5.75 million units of the official Rubik’s Cube were sold globally and that figure was up 14% year-to-date, according to ...
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The projection center has 2 cube corners, so there are (8+6) 14 spheres in 3D space of this cube. A last copy has larger spheres/circles which might be harder to see. So the 3D presentation the connection to the cube and octahedron are apparent. The cube vertices are the 8 blue spheres, and the octahedron vertices are the cube face centers.