concave polyhedron
Definition
- Noun:
- A polyhedron with at least one concave face or interior angle: A three-dimensional solid figure bounded by polygons, where at least one of its faces is a concave polygon, or where at least one interior dihedral angle is greater than 180 degrees. This means that if you were to draw a line segment connecting two points inside the polyhedron, the segment might lie partially outside the polyhedron's volume.
Usage
- Noun:
- A concave polyhedron, unlike a convex one, can have indentations or cavities.
- The shape of a star or a bowl-like structure can often be modeled as a concave polyhedron.
Advanced Usage
- In geometry and modeling: The term is used to classify 3D shapes in computational geometry, 3D modeling, and mathematics, distinguishing them from convex polyhedra where all interior angles are less than 180 degrees and all line segments between points lie entirely within the shape.
- The algorithm must handle both convex and concave polyhedra for realistic physical simulation.
Variants and Related Words
- Polyhedron (n): A solid figure with many plane faces, typically more than six.
- Concave polygon (n): A two-dimensional polygon with at least one interior angle greater than 180°, which is the 2D equivalent.
- Convex polyhedron (n): A polyhedron where any line segment joining two points within it lies entirely inside it; the opposite of a concave polyhedron.
Synonyms
- Non-convex polyhedron: A more general term that includes concave polyhedra.
- Re-entrant polyhedron: An older term sometimes used synonymously with concave polyhedron.
Related Concepts
- Euler's Formula: A theorem relating the number of faces (F), vertices (V), and edges (E) of a polyhedron (V - E + F = 2), which also applies to simple concave polyhedra.
- Dihedral angle: The angle between two intersecting planes, crucial for determining if a polyhedron is concave.
Noun
-
a polyhedron some of whose plane sections are concave polygons
