DODECAHEDRON (Gr. δώδεκα, twelve, and ἕδρα, a face or base), in geometry, a solid enclosed by twelve plane faces. The “ordinary dodecahedron” is one of the Platonic solids (see [Polyhedron]). The Greeks discovered that if a line be divided in extreme and mean proportion, then the whole line and the greater segment are the lengths of the edge of a cube and dodecahedron inscriptible in the same sphere. The “small stellated dodecahedron,” the “great dodecahedron” and the “great stellated dodecahedron” are Kepler-Poinsot solids; and the “truncated” and “snub dodecahedra” are Archimedean solids (see [Polyhedron]). In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the “pentagonal dodecahedron” of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones. The “rhombic dodecahedron,” one of the geometrical semiregular solids, is an important crystal form. Many other dodecahedra exist as crystal forms, for which see Crystallography.
DODECASTYLE (Gr. δώδεκα, twelve, and στῦλος, column), the architectural term given to a temple where the portico has twelve columns in front, as in the portico added to the temple of Demeter at Eleusis, designed by Philo, the architect of the arsenal at the Peiraeus.
DÖDERLEIN, JOHANN CHRISTOPH WILHELM LUDWIG (1791-1863), German philologist, was born at Jena on the 19th of December 1791. His father, Johann Christoph Döderlein, professor of theology at Jena, was celebrated for his varied learning, for his eloquence as a preacher, and for the important influence he exerted in guiding the transition movement from strict orthodoxy to a freer theology. Ludwig Döderlein, after receiving his preliminary education at Windsheim and Schulpforta (Pforta), studied at Munich, Heidelberg, Erlangen and Berlin. He devoted his chief attention to philology under the instruction of such men as F. Thiersch, G. F. Creuzer, J. H. Voss, F. A. Wolf, August Böckh and P. K. Buttmann. In 1815, soon after completing his studies at Berlin, he accepted the appointment of ordinary professor of philology in the academy of Bern. In 1819 he was transferred to Erlangen, where he became second professor of philology in the university and rector of the gymnasium. In 1827 he became first professor of philology and rhetoric and director of the philological seminary. He died on the 9th of November 1863. Döderlein’s most elaborate work as a philologist was marred by over-subtlety, and lacked method and clearness. He is best known by his Lateinische Synonymen und Etymologien (1826-1838), and his Homerisches Glossarium (1850-1858). To the same class belong his Lateinische Wortbildung (1838), Handbuch der lateinischen Synonymik (1839), and the Handbuch der lateinischen Etymologie (1841), besides various works of a more elementary kind intended for the use of schools and gymnasia. Most of the works named have been translated into English. To critical philology Döderlein contributed valuable editions of Tacitus (Opera, 1847; Germania, with a German translation) and Horace (Epistolae, with a German translation, 1856-1858; Satirae, 1860). His Reden und Aufsätze (Erlangen, 1843-1847) and Offentliche Reden (1860) consist chiefly of academic addresses dealing with various subjects in paedagogy and philology.
DODGE, THEODORE AYRAULT (1842-1909), American soldier and military writer, was born at Pittsfield, Massachusetts, on the 28th of May 1842. He received a military education in Germany and subsequently studied at Heidelberg and London University, returning to the United States in 1861. At the outbreak of the Civil War he at once enlisted in the federal army, and he soon rose to commissioned rank. He served in the Army of the Potomac until Gettysburg, where he lost a leg. Incapacitated for further active service, he continued to be employed in administrative posts to the end of the war, and for several years thereafter he served at army headquarters, becoming captain in 1866 and brevet lieutenant-colonel in 1867. He retired in 1870. His works include The Campaign of Chancellorsville (1881), A Bird’s Eye View of our Civil War (1882, later edition 1897), a complete, accurate and remarkably concise account of the whole war, Patroclus and Penelope, a Chat in the Saddle (1883), Great Captains (1886), a series of lectures, Riders of Many Lands (1893), and a series of large illustrated volumes entitled A History of the Art of War, being lives of “Great Captains,” including Alexander (2 vols., 1888), Hannibal (2 vols., 1889), Caesar (2 vols., 1892), Gustavus Adolphus (2 vols., 1896) and Napoleon (4 vols., 1904-1907). He died in France, at Versailles, on the 26th of October 1909.
DODGSON, CHARLES LUTWIDGE [”Lewis Carroll”] (1832-1898), English mathematician and author, son of the Rev. Charles Dodgson, vicar of Daresbury, Cheshire, was born in that village on the 27th of January 1832. The literary life of “Lewis Carroll” became familiar to a wide circle of readers, but the private life of Charles Lutwidge Dodgson was retired and practically uneventful. After four years’ schooling at Rugby, Dodgson matriculated at Christ Church, Oxford, in May 1850; and from 1852 till 1870 held a studentship there. He took a first class in the final mathematical school in 1854, and the following year was appointed mathematical lecturer at Christ Church, a post he continued to fill till 1881. In 1861 he was ordained deacon, but he never took priest’s orders, possibly because of a stammer which prevented reading aloud. His earliest publications, beginning with A Syllabus of Plane Algebraical Geometry (1860) and The Formulae of Plane Trigonometry (1861), were exclusively mathematical; but late in the year 1865 he published, under the pseudonym of “Lewis Carroll,” Alice’s Adventures in Wonderland, a work that was the outcome of his keen sympathy with the imagination of children and their sense of fun. Its success was immediate, and the name of “Lewis Carroll” has ever since been a household word. A dramatic version of the “Alice” books by Mr Savile Clarke was produced at Christmas, 1886, and has since enjoyed many revivals. Mr Dodgson was always very fond of children, and it was an open secret that the original of “Alice” was a daughter of Dean Liddell. Alice was followed (in the “Lewis Carroll” series) by Phantasmagoria, in 1869; Through the Looking-Glass, in 1871; The Hunting of the Snark (1876); Rhyme and Reason (1883); A Tangled Tale (1885); and Sylvie and Bruno (in two parts, 1889 and 1893). He wrote skits on Oxford subjects from time to time. The Dynamics of a Particle was written on the occasion of the contest between Gladstone and Mr Gathorne Hardy (afterwards earl of Cranbrook); and The New Belfry in ridicule of the erection put up at Christ Church for the bells that were removed from the Cathedral tower. While “Lewis Carroll” was delighting children of all ages, C. L. Dodgson periodically published mathematical works—An Elementary Treatise on Determinants (1867); Euclid, Book V., proved Algebraically (1874); Euclid and his Modern Rivals (1879), the work on which his reputation as a mathematician largely rests; and Curiosa Mathematica (1888). Throughout this dual existence Mr Dodgson pertinaciously refused to acquiesce in being publicly identified with “Lewis Carroll.” Though the fact of his authorship of the “Alice” books was well known, he invariably stated, when occasion called for such a pronouncement, that “Mr Dodgson neither claimed nor acknowledged any connexion with the books not published under his name.” He died at Guildford, on the 14th of January 1898. His memory is appropriately kept green by a cot in the Children’s Hospital, Great Ormond Street, London, which was endowed perpetually by a public subscription.
See S. D. Collingwood, Life and Letters of Lewis Carroll (1898).