different between polyhedron vs disphenoid

English

Alternative forms

• polyedron

Etymology

From New Latin, from Ancient Greek ????????? (polúedron), from ????? (polús, “many”) + ???? (hédra, “seat”); compare French polyèdre.

Pronunciation

• (UK) enPR: p?l?h?'dr?n, IPA^(key): /p?li?hi?d??n/

Noun

polyhedron (plural polyhedra or polyhedrons)

1. (geometry) A solid figure with many flat faces and straight edges.
2. (optics) A polyscope, or multiplying glass.

Hypernyms

• abstract polyhedron
• polytope

Hyponyms

See also Thesaurus:polyhedron

Translations

See also

• apeirohedron
• Schläfli symbol
• spherical polyhedron
• subpolyhedron
• tessellation

English

Etymology

From di- (“twice, double”) +? sphenoid (“wedge-shaped crystal or bone of the skull”).

Adjective

disphenoid (not comparable)

1. (mineralogy) Of or pertaining to a wedge-shaped crystal form of the tetragonal or orthorhombic system.
2. (mineralogy) Of or pertaining to a crystal form bounded by eight scalene triangles arranged in pairs, constituting a tetragonal scalenohedron.

Noun

disphenoid (plural disphenoids)

1. (geometry) A non-regular tetrahedron whose four faces are congruent acute-angled triangles.
   • 1973, H. S. M. Coxeter, 3rd Edition, unnumbered page,

     To make a model of a disphenoid, cut out an acute angled triangle and fold it along the joins of the mid-points of the sides. The disphenoid is said to be rhombic or tetragonal according as the triangle is isosceles or scalene.

   • 1977, Elizabeth A. Wood, Crystals and Light: An Introduction to Optical Crystallography, 2nd Revised Edition, page 8,

     If you rotate the [tetragonal] disphenoid 90° around its 2-fold axis and then perform the operation of inversion through the center-point of the object, it will occupy its original position again.

   • 1993, Horst Martini, A Hierarchical Classification of Euclidean Polytopes with Regularity Properties, Tibor Bisztriczky, Peter McMullen, Rolf Schneider, Asia Ivic Weiss (editors), Polytopes: Abstract, Convex and Computational, Proceedings of the NATO Advanced Study Institute, page 83,

     In addition it should be remarked that there are two types of disphenoids, with different symmetries: the tetragonal disphenoid (having isosceles facets) and the rhombic one.

Synonyms

• (non-regular tetrahedron with congruent faces): bisphenoid, equifacial tetrahedron, isosceles tetrahedron

Derived terms

• rhombic disphenoid
• snub disphenoid
• tetragonal disphenoid