Thursday, December 17, 2009

Acronym in geometry: SCCO for small cubi-cuboctahedron

SCCO stands for small cubi-cuboctahedron (also non-hyphenated: small cubicuboctahedron). The SCCO is one of the 43 polyhedra collectively known as nonconvex uniform polyhedra (n-cUP). The mathematician John Lawrence Hudson illustrated the geometry and stellation of the SCCO in a recent article [1], pointing to the component forms (Platonic polyhedra) that are reflected in its name: six facial planes containing a square lying in the planes of a cube, eight facial planes containing a triangle lying in the planes of an octahedron, and six facial planes containing an octagon lying again in the planes of a cube. The latter cube is smaller than the first and lies therein with its facial planes parallel to corresponding planes of the first cube. The adjective “small” in SCCO distinguishes this solid from the “great” cubi-cuboctahedron.
The SCCO symmetry group: octahedral (also reflected in the name). Since the SCCO has three face types (equilateral triangle, square, and regular octagon), it has three different stellation diagrams.

Keywords: three-dimensional geometry, polytopes, solids, facial planes, 2-D facets

References and illustrations
[1] John Lawrence Hudson: Further Stellations of the Uniform Polyhedra. The Mathematical Intelligencer Fall 2009, Volume 31, No. 4, pp. 18-26.

Tuesday, December 15, 2009

The name dinosaur from the Greek words deinos (terrible) and sauros (lizard)

The name dinosaur (“terrible lizard”) was coined in the years after 1841 by the English biologist and palaeontologist Sir Richard Owen (1804-1892) [1,2]. Karl-Heinz Ludwig includes a small paragraph entitled Wie die Dinos zu ihrem Namen kamen (How the dinos got their name) in his book on climate change through the history of the Earth. Based on this German-language text [2] and information in Christopher McGowan's captivating book about prehistoric reptiles [1], the following summary can be shaped:

The word dinosaur, composed of the Greek words deinos (terrible) and sauros (lizard), first occurred in a publication by Richard Owen in 1842: Report on British fossil reptiles. Part II. Report of the British Association for the Advancement of Science, Plymouth, 11:60-204. By comparing fossil bones of Iguanodon (“iguana tooth”, an ornithopod), Megalosaurus (“big lizard”, a theropod) and Hylaeosaurus (“woodland lizard”, an ankylosaur), which had been discovered by William Buckland and Gideon Mantell in southern England, Owen recognized that these fossils represented a new group of Mesozoic reptiles. The classification of dinosaurs is not completed and the discovery of new dinosaur fossils and/or novel species can be expected to make news headlines any day.

Keywords: history, palaeontology, comparative anatomy, Mesozoic Era

[1] Christopher McGowan:
Dinosaurs, Spitfires, & Sea Dragons. Harvard University Press, Cambridge, Massachusetts and London England, 1992 (first paperback edition); pages 190 and 343.
[2] Karl-Heinz Ludwig:
Eine kurze Geschichte des KlimasVon der Entstehung der Erde bis heute. Verlag C. H. Beck oHG, München, 2006; page 46.