parallelopipedon
Definition
- Noun:
- A solid geometric figure with six faces, each of which is a parallelogram: A "parallelopipedon" is a three-dimensional shape, specifically a prism, where all six faces are parallelograms. This means opposite faces are parallel and identical in shape and size.
Usage
- The term is used in geometry and mathematics to describe a specific type of polyhedron.
- It is a formal, technical term. In more common usage, the word "parallelepiped" is often preferred.
Examples
- Noun:
- The crystal's structure was that of a perfect parallelopipedon.
- In the geometry problem, we had to calculate the volume of a parallelopipedon.
Advanced Usage
- The word is synonymous with parallelepiped. "Parallelopipedon" is an older, less common variant.
- It can be described by three vectors originating from the same vertex, representing its edges.
Variants and Related Words
- Parallelepiped (n): The more common modern spelling for the same geometric solid.
- Prism (n): A broader category of polyhedron; a parallelopipedon is a specific type of prism with parallelogram bases.
- Hexahedron (n): Any polyhedron with six faces; a cube and a parallelopipedon are both hexahedrons.
Synonyms
- Parallelepiped: A solid figure bounded by six parallelograms.
- Oblique prism (with parallelogram bases): Describes the shape when it is not a right prism (where lateral faces are rectangles).
Related Terms and Concepts
- Rectangular Parallelepiped: A special case where all angles are right angles, making all faces rectangles. This is commonly known as a rectangular prism or a cuboid.
- Volume Calculation: The volume of a parallelopipedon can be found using the scalar triple product of the three vectors defining its edges.
Noun
-
a prism whose bases are parallelograms
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