hexakisoctahedron

plural hexakisoctahedra · plural hexakisoctahedrons

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

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

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

   3 more examples

   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.

   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 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.

   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

   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.

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

   Synonyms: hexoctahedron, tetracontaoctahedron