hexakisoctahedron

English

Etymology

From hexakis- +‎ octahedron.

Noun

hexakisoctahedron (plural hexakisoctahedra or hexakisoctahedrons)

1. A three-dimensional solid with 48 faces arranged around 9 planes of reflection and 13 rotary axes.

   Synonyms: hexoctahedron, tetracontaoctahedron

   • 1841, John Joseph Griffin, “Principles of Crystallography”, in A System of Crystallography, with Its Application to Mineralogy, Glasgow: Richard Griffin and Company. And Thomas Tegg, London, section XIII (An Inquiry into the variety of Forms and Combinations which occur upon the Crystals of Minerals), subsection I (The Octahedral System of Crystallisation), subsubsection 4 (The Hemihexakisoctahedron with inclined faces), § 450, page 217:

     The second is a hemihedral combination of which no corresponding homohedral variety has been discovered, and no hemihexakisoctahedrons have been found to correspond with the rest of the known hexakisoctahedrons, § 408.

   • 1881, Hilary Bauerman, “Cubic System”, in Text-Book of Systematic Mineralogy, New York, N.Y.: D. Appleton and Co., page 52:

     The plagihedral hemihedral forms of the cubis system are, with the exception of those derivable from hexakisoctahedra, undistinguishable from the holohedral forms.

   • 1995, R. E. Smallman, R. J. Bishop, “Atomic arrangements in materials”, in Metals and Materials: Science, Processes, Applications, Butterworth-Heinemann, section 5 (Selected crystal structures), subsection 5 (Silica), page 25:

     The plane (1 2 3), which is an example of the most general crystal plane in the cubic system because its hkl indices are all different, lies between (1 1 2) and (0 1 1) planes; the 48 planes of the {1 2 3} form make up a hexakisoctahedron.

   • 2003, Christian Bök, Crystallography, 2nd edition, Coach House Books, published June 2006, →ISBN, page 141:

     A crystalline spectrum maps the æsthetic value of all stylistic paragons – from isometric order in classicism to triclinic disorder in modernism: the hexakisoctahedron being most symmetric of all the crystal habits, its thirteen rotary axes & nine reflexive planes, for its four dozen facets, rigidest rhyme scheme – an ideal form driving insane every scientific monk who inhabits its polyhedral cathedrals, almost every organism a bilateral construction divided against itself, almost every organism a bilateral construction divided against itself, almost every particle a planet spinning two times for every sunset.

Derived terms

• hemihexakisoctahedron

Translations

geometry — see hexoctahedron