Definition

Noun: 1. A polyhedron whose faces are trapeziums (trapezoids): In geometry, a trapezohedron is a solid figure (polyhedron) where every face is a trapezium (a quadrilateral with at least one pair of parallel sides). This term is most specifically used for a particular class of polyhedra known as deltoidal or tetragonal trapezohedra, which are the dual polyhedra to antiprisms.

Examples of Usage

• Noun:
  • The crystal exhibited a perfect trapezohedron form.
  • In his geometry class, he constructed a model of a trapezohedron.
  • The mineral's structure is that of a trigonal trapezohedron.

Advanced Usage

• Crystallography: In this field, "trapezohedron" refers to a specific crystal habit (the common shape of a crystal) where the crystal faces are trapeziums. Terms like or describe the crystal's symmetry class.
  • The quartz crystal displayed a distinctive trigonal trapezohedron habit.

Variants and Related Words

• Trapezohedral (adj): Having the form of a trapezohedron.
  • The gem was cut into a trapezohedral shape.

Synonyms

• Deltohedron: A more specific term sometimes used interchangeably for the dual of an antiprism.
• Antiprism dual: A description of its geometric relationship rather than a direct synonym.

Notes on Meaning

The term "trapezohedron" is highly specialized to geometry and crystallography. Its defining characteristic is that all faces are quadrilaterals known as trapeziums (or trapezoids). It is not a common polyhedron like a cube or pyramid.

Noun

1. a polyhedron whose faces are trapeziums