# rhombicosidodecahedron
## English
### Etymology

* PIE word
* *déḱm̥
Learned borrowing from New Latin rhombicosidodecaēdron (coined by the German astronomer and mathematician Johannes Kepler (1571–1630) in his work Harmonices Mundi Libri V (The Harmony of the World in Five Books, 1619)), a blend of Latin rhomb(us) + īcos(aedron) + -i- + dodecaēdron. The English word is analysable as a blend of rhomb(ic) +‎ icosidodecahedron, referring to the fact that the 30 square faces lie in the same planes as the 30 rhombic faces of the rhombic triacontahedron, which is dual to the icosidodecahedron.

### Pronunciation

* Singular:
** (Received Pronunciation) IPA: /ˌɹɒmbaɪˌkəʊsidəʊˌdɛkəˈhiːdɹən/, /ˌɹɒmbɪ-/
** Audio (Southern England):(file)
** (General American) IPA: /ˌɹɑmbaɪˌkoʊsidoʊˌdɛkəˈhidɹən/, /ˌɹɑmbə-/
** Rhymes: -iːdɹən
** Hyphenation: rhomb‧i‧co‧si‧do‧dec‧a‧he‧dron
* Plural (rhombicosidodecahedra):
** (Received Pronunciation) IPA: /ˌɹɒmbaɪˌkəʊsidəʊˌdɛkəˈhiːdɹə/, /ˌɹɒmbɪ-/
** (General American) IPA: /ˌɹɑmbaɪˌkoʊsidoʊˌdɛkəˈhidɹə/, /ˌɹɑmbə-/
** Hyphenation: rhomb‧i‧co‧si‧do‧dec‧a‧he‧dra

### Noun

rhombicosidodecahedron (plural rhombicosidodecahedra or rhombicosidodecahedrons)
* (geometry) An Archimedean solid with 62 regular faces (20 triangles, 30 squares, and 12 pentagons), 60 vertices and 120 edges.
    Synonym: small rhombicosidodecahedron
** 1889, “Archimedean, a.”, in William Dwight Whitney, editor, The Century Dictionary: An Encyclopedic Lexicon of the English Language […], volume I, New York, N.Y.: The Century Co., →OCLC, page 297, column 1:Archimedean solid, one of the thirteen solids described by Archimedes, which, without being regular, have all their solid angles alike, all their faces regular, and not less than four faces of any one kind; […] They are […] the rhombicosidodecahedron, the truncated icosidodecahedron, and the snub-dodecahedron.
** 1989, P. W. Messer, M[agnus] J[oseph] Wenninger, “Symmetry and Polyhedral Stellation—II”, in Computers & Mathematics with Applications, volume 17, numbers 1–3, Oxford, Oxfordshire: Pergamon Press, →DOI, →ISSN, →OCLC, page 195; reprinted in István Hargittai, editor, Symmetry 2: Unifying Human Understanding (International Series in Modern Applied Mathematics and Computer Science; 18), Oxford, Oxfordshire: Pergamon Press, 1989, →ISBN, part 1, page 195:The purpose of this article is to offer a method of approach for investigating the stellation pattern of the deltoidal hexecontahedron, the dual of the rhombicosidodecahedron.
** 1994, Steven Schwartzman, “rhombicosidodecahedron”, in The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: 2:Mathematical Association of America, →DOI, →ISBN, page 189, column 1:There are two distinct rhombicosidodecahedra, one bearing the unmodified name and the other called the great rhombicosidodecahedron. Like the rhombus, the icosahedron and the dodecahedron, all of the great rhombicosidodecahedron’s 62 faces are either [square] rhombi (30), equilateral triangles (20) or regular pentagons (12).
** 1996, Hugo F[rançois] Verheyen, “Groups of Isometries”, in Symmetry Orbits (Design Science Collection), Boston, Mass.; Basel, Basel-Stadt: Birkhäuser, →DOI, →ISBN, part I (Realization of Symmetry Groups), page 37:Next, the totality of 31 axes is illustrated in a rhombicosidodecahedron, an Archimedean solid composed of 30 squares, 20 triangles, and 12 pentagons […], with a view to the inside of the model showing the center of the group, the point of invariancy $O$ […] Finally, the other dihedral subgroups are also illustrated on a rhombicosidodecahedron: $D_{3}$ of order 6 and index 10 […] and $D_{5}$ of order 10 and index 6 […].
** 2014, Thomasenia Lott Adams, Joanne LaFramenta, “Conclusion”, in Math Know-how: Answers to Your Most Persistent Teaching Issues, Grades 3–5, Thousand Oaks, Calif.; London: Corwin, SAGE Publications, →ISBN, page 172:[…] I noticed that the little balls (rhombicosidodecahedrons) had openings shaped in the form of triangles, rectangles, and pentagons.

#### Derived terms

* great rhombicosidodecahedron
* nonconvex great rhombicosidodecahedron
* quasirhombicosidodecahedron
* small rhombicosidodecahedron

#### Related terms

* dodecahedron
* icosahedron
* icosidodecahedron
* rhombohedron

#### Translations
### References

* ↑ Ioannis Keppler [i.e., Johannes Kepler] (1619) “Liber II. De Congruentia Figurarum Harmonicarum. XXVIII. Propositio. [Book II. On the Congruence of Harmonic Figures. Proposition XXVIII.]”, in Harmonices Mundi Libri V [The Harmony of the World in Five Books], Linz, Austria: Sumptibus Godofredi Tampachii bibl. Francof. excudebat Ioannes Plancus [published by Gottfried Tambach [...] printed by Johann Planck], →OCLC, page 64: “Unus igitur Trigonicus cum duobus Tetragonicis & uno Pentagonico, minus efficiunt 4 rectis, & congruunt 20 Trigonicum 30 Tetragonis & 12 Pentagonis, in unum Hexacontadyhedron, quod appello Rhombicoſidodecaëdron, ſeu ſectum Rhombum Icoſidododecaëdricum. ― Therefore, one trigon with two tetragons and one pentagon, makes fewer than 4 straight lines, and 20 trigons correspond to 30 tetragons and 12 pentagons into one hexacontadyhedron, which I call the rhombicosidodecahedron, or the truncated icosidodecahedral rhombus.”
* ↑ Compare Steven Schwartzman (1994) “rhombicosidodecahedron”, in The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: 2:Mathematical Association of America, →DOI, →ISBN, page 189, column 1.

### Further reading

* rhombicosidodecahedron on Wikipedia.Wikipedia