MHB How to Determine Orientation in 3-Dimensional Space?

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In three-dimensional space, orientation can be determined by analyzing the arrangement of an object's vertices. For solids like cubes and tetrahedrons, vertices can be labeled to establish their positions; for instance, a cube's vertices can be labeled A, B, C, D for the top plane and E, F, G, H for the bottom. The orientation of each vertex is assessed based on its relative position to others, with specific viewing angles influencing whether the orientation appears clockwise or counter-clockwise. This method allows for a clear understanding of spatial orientation in 3D geometry. Proper labeling and analysis of vertex positions are essential for accurately determining orientation in three-dimensional objects.
Amer
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In 2 dimensions we have clockwise and counter clockwise orientation, in 3 dimensions how to determine orientation in the space.
for example: how to name the vertices of a solid like a cube or a tetrahedron.
 
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The orientation of a 3-dimensional object can be determined by looking at the orientation of its vertices. For example, the vertices of a cube can be labeled A, B, C, D, E, F, G and H, with ABCD being on the top plane and EFGH being the bottom plane. The orientation of each vertex can then be determined by its position relative to the other vertices. For example, vertex A would be oriented in a counter-clockwise direction if viewed from above, while vertex B would be oriented in a clockwise direction if viewed from the same angle. Similarly, the vertices of a tetrahedron can be labeled A, B, C and D, with the orientation of each vertex determined by its position relative to the other vertices.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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