different between scalenohedron vs disphenoid

English

Etymology

scalene +? -o- +? -hedron

Noun

scalenohedron (plural scalenohedrons or scalenohedra)

1. (geometry, mineralogy, crystallography) A polyhedron having twelve sides, each in the form of a scalene triangle, that is topologically equivalent to a hexagonal bipyramid and whose middle section can be said to inscribe a rhombohedron.
   • 1859, James Tennant, Walter Mitchell, Mineralogy and Crystallography: Being a Classification of Crystals According to Their Form, page 408,

     Though the hexagonal scalenohedron is derived from the double twelve-faced pyramid, by the development of half its faces, and might be constructed from that figure, it is more readily obtained from the positive or negative rhomboid which may be supposed to be inscribed in the scalenohedron.

   • 1907, Benjamin K. Emerson, Joseph H. Perry, The Green Schists and Associated Granites and Porphyries of Rhode Island, US Geological Survey, Bulletin Number 311, page 24,

     Other steep scalenohedrons of the principal zone are also often present, sometimes in addition to y, sometimes taking its place.

   • 1940, John W. Evans, George MacDonald Davies, Elementary Crystallography, page 111,

     Calcite crystals show a great variety of habits — acute and obtuse rhombohedra and scalenohedra, prisms, and thin tabular forms.

Related terms

• scalenohedral

See also

• star bipyramid

Further reading

• Bipyramid#Scalenohedron on Wikipedia.Wikipedia
• Scalenohedron, in Wolfram Demonstrations Project

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