/* * $Id: Uniform.java,v 1.79 2007/02/09 20:13:31 rl Exp $ ********************************************************** * kaleido * * Kaleidoscopic construction of uniform polyhedra * Copyright © 1991-2007 Dr. Zvi Har’El * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. The end-user documentation included with the redistribution, * if any, must include the following acknowledgment: * “This product includes software developed by * Dr. Zvi Har’El (http://www.math.technion.ac.il/~rl/).” * Alternately, this acknowledgment may appear in the software itself, * if and wherever such third-party acknowledgments normally appear. * * This software is provided ‘as-is’, without any express or implied * warranty. In no event will the author be held liable for any * damages arising from the use of this software. * * Author: * Dr. Zvi Har’El, * Deptartment of Mathematics, * Technion, Israel Institue of Technology, * Haifa 32000, Israel. * E-Mail: rl@math.technion.ac.il ********************************************************** */ package kaleido; /** * List of Uniform Polyhedra and Their Kaleidoscopic Formulae. *

* Each entry contains the following items: *

    *
  1. Wythoff symbol. *
  2. Polyhedron name. *
  3. Dual name. *
  4. Coxeter et al. reference figure. *
  5. Wenninger reference figure. *
*

* Notes: *

    *
  1. Cundy and Roulette’s trapezohedron has been renamed to deltohedron, as * its faces are deltoids, not trapezoids. *
  2. The names of the non-dihedral polyhedra are those which appear in * Wenninger (1984). Some of them are slightly modified versions of those * in Wenninger (1971). *
*

* References: *

*
Coxeter, H.S.M., Longuet-Higgins, M.S. and Miller, J.C.P., *
Uniform polyhedra, Phil. Trans. Royal Soc. London, Ser. A, * 246 (1953), 401-409. *
Cundy, H.M. and Rollett, A.P., *
“Mathematical Models”, 3rd Ed., Tarquin, 1981. *
Har’El, Z. *
* Uniform Solution for Uniform Polyhedra, Geometriae * Dedicata, 47 (1993), 57-110. *
Wenninger, M.J., *
“Polyhedron Models”, Cambridge University Press, 1971. *
“Dual Models”, Cambridge University Press, 1984. *
* @author Zvi Har’El * @version $Id: Uniform.java,v 1.79 2007/02/09 20:13:31 rl Exp $ * @see Class source code */ public class Uniform { public static final Entry[] list = { /****************************************************************************** * Dihedral Schwarz Triangles (D5 only) ******************************************************************************/ /* (2 2 5) (D1/5) */ /*1*/ new Entry ("2 5|2","pentagonal prism", "pentagonal dipyramid",0,0), /*2*/ new Entry("|2 2 5","pentagonal antiprism", "pentagonal deltohedron",0,0), /* (2 2 5/2) (D2/5) */ /*3*/ new Entry("2 5/2|2","pentagrammic prism", "pentagrammic dipyramid",0,0), /*4*/ new Entry("|2 2 5/2","pentagrammic antiprism", "pentagrammic deltohedron",0,0), /* (5/3 2 2) (D3/5) */ /*5*/ new Entry("|2 2 5/3","pentagrammic crossed antiprism", "pentagrammic concave deltohedron",0,0), /******************************************************************************* * Tetrahedral Schwarz Triangles *******************************************************************************/ /* (2 3 3) (T1) */ /*6*/ new Entry("3|2 3","tetrahedron", "tetrahedron",15,1), /*7*/ new Entry("2 3|3","truncated tetrahedron", "triakistetrahedron",16,6), /* (3/2 3 3) (T2) */ /*8*/ new Entry("3/2 3|3","octahemioctahedron", "octahemioctacron",37,68), /* (3/2 2 3) (T3) */ /*9*/ new Entry("3/2 3|2","tetrahemihexahedron", "tetrahemihexacron",36,67), /****************************************************************************** * Octahedral Schwarz Triangles ******************************************************************************/ /* (2 3 4) (O1) */ /*10*/ new Entry("4|2 3","octahedron", "cube",17,2), /*11*/ new Entry("3|2 4","cube", "octahedron",18,3), /*12*/ new Entry("2|3 4","cuboctahedron", "rhombic dodecahedron",19,11), /*13*/ new Entry("2 4|3","truncated octahedron", "tetrakishexahedron",20,7), /*14*/ new Entry("2 3|4","truncated cube", "triakisoctahedron",21,8), /*15*/ new Entry("3 4|2","rhombicuboctahedron", "deltoidal icositetrahedron",22,13), /*16*/ new Entry("2 3 4|","truncated cuboctahedron", "disdyakisdodecahedron",23,15), /*17*/ new Entry("|2 3 4","snub cube", "pentagonal icositetrahedron",24,17), /* (3/2 4 4) (O2b) */ /*18*/ new Entry("3/2 4|4","small cubicuboctahedron", "small hexacronic icositetrahedron",38,69), /* (4/3 3 4) (O4) */ /*19*/ new Entry("3 4|4/3","great cubicuboctahedron", "great hexacronic icositetrahedron",50,77), /*20*/ new Entry("4/3 4|3","cubohemioctahedron", "hexahemioctacron",51,78), /*21*/ new Entry("4/3 3 4|","cubitruncated cuboctahedron", "tetradyakishexahedron",52,79), /* (3/2 2 4) (O5) */ /*22*/ new Entry("3/2 4|2","great rhombicuboctahedron", "great deltoidal icositetrahedron",59,85), /*23*/ new Entry("3/2 2 4|","small rhombihexahedron", "small rhombihexacron",60,86), /* (4/3 2 3) (O7) */ /*24*/ new Entry("2 3|4/3","stellated truncated hexahedron", "great triakisoctahedron",66,92), /*25*/ new Entry("4/3 2 3|","great truncated cuboctahedron", "great disdyakisdodecahedron",67,93), /* (4/3 3/2 2) (O11) */ /*26*/ new Entry("4/3 3/2 2|","great rhombihexahedron", "great rhombihexacron",82,103), /****************************************************************************** * Icosahedral Schwarz Triangles ******************************************************************************/ /* (2 3 5) (I1) */ /*27*/ new Entry("5|2 3","icosahedron", "dodecahedron",25,4), /*28*/ new Entry("3|2 5","dodecahedron", "icosahedron",26,5), /*29*/ new Entry("2|3 5","icosidodecahedron", "rhombic triacontahedron",28,12), /*30*/ new Entry("2 5|3","truncated icosahedron", "pentakisdodecahedron",27,9), /*31*/ new Entry("2 3|5","truncated dodecahedron", "triakisicosahedron",29,10), /*32*/ new Entry("3 5|2","rhombicosidodecahedron", "deltoidal hexecontahedron",30,14), /*33*/ new Entry("2 3 5|","truncated icosidodechedon", "disdyakistriacontahedron",31,16), /*34*/ new Entry("|2 3 5","snub dodecahedron", "pentagonal hexecontahedron",32,18), /* (5/2 3 3) (I2a) */ /*35*/ new Entry("3|5/2 3","small ditrigonal icosidodecahedron", "small triambic icosahedron",39,70), /*36*/ new Entry("5/2 3|3","small icosicosidodecahedron", "small icosacronic hexecontahedron",40,71), /*37*/ new Entry("|5/2 3 3","small snub icosicosidodecahedron", "small hexagonal hexecontahedron",41,110), /* (3/2 5 5) (I2b) */ /*38*/ new Entry("3/2 5|5","small dodecicosidodecahedron", "small dodecacronic hexecontahedron",42,72), /* (2 5/2 5) (I3) */ /*39*/ new Entry("5|2 5/2","small stellated dodecahedron", "great dodecahedron",43,20), /*40*/ new Entry("5/2|2 5","great dodecahedron", "small stellated dodecahedron",44,21), /*41*/ new Entry("2|5/2 5","great dodecadodecahedron", "medial rhombic triacontahedron",45,73), /*42*/ new Entry("2 5/2|5","truncated great dodecahedron", "small stellapentakisdodecahedron",47,75), /*43*/ new Entry("5/2 5|2","rhombidodecadodecahedron", "medial deltoidal hexecontahedron",48,76), /*44*/ new Entry("2 5/2 5|","small rhombidodecahedron", "small rhombidodecacron",46,74), /*45*/ new Entry("|2 5/2 5","snub dodecadodecahedron", "medial pentagonal hexecontahedron",49,111), /* (5/3 3 5) (I4) */ /*46*/ new Entry("3|5/3 5","ditrigonal dodecadodecahedron", "medial triambic icosahedron",53,80), /*47*/ new Entry("3 5|5/3","great ditrigonal dodecicosidodecahedron", "great ditrigonal dodecacronic hexecontahedron",54,81), /*48*/ new Entry("5/3 3|5","small ditrigonal dodecicosidodecahedron", "small ditrigonal dodecacronic hexecontahedron",55,82), /*49*/ new Entry("5/3 5|3","icosidodecadodecahedron", "medial icosacronic hexecontahedron",56,83), /*50*/ new Entry("5/3 3 5|","icositruncated dodecadodecahedron", "tridyakisicosahedron",57,84), /*51*/ new Entry("|5/3 3 5","snub icosidodecadodecahedron", "medial hexagonal hexecontahedron",58,112), /* (3/2 3 5) (I6b) */ /*52*/ new Entry("3/2|3 5","great ditrigonal icosidodecahedron", "great triambic icosahedron",61,87), /*53*/ new Entry("3/2 5|3","great icosicosidodecahedron", "great icosacronic hexecontahedron",62,88), /*54*/ new Entry("3/2 3|5","small icosihemidodecahedron", "small icosihemidodecacron",63,89), /*55*/ new Entry("3/2 3 5|","small dodecicosahedron", "small dodecicosacron",64,90), /* (5/4 5 5) (I6c) */ /*56*/ new Entry("5/4 5|5","small dodecahemidodecahedron", "small dodecahemidodecacron",65,91), /* (2 5/2 3) (I7) */ /*57*/ new Entry("3|2 5/2","great stellated dodecahedron", "great icosahedron",68,22), /*58*/ new Entry("5/2|2 3","great icosahedron", "great stellated dodecahedron",69,41), /*59*/ new Entry("2|5/2 3","great icosidodecahedron", "great rhombic triacontahedron",70,94), /*60*/ new Entry("2 5/2|3","great truncated icosahedron", "great stellapentakisdodecahedron",71,95), /*61*/ new Entry("2 5/2 3|","rhombicosahedron", "rhombicosacron",72,96), /*62*/ new Entry("|2 5/2 3","great snub icosidodecahedron", "great pentagonal hexecontahedron",73,113), /* (5/3 2 5) (I9) */ /*63*/ new Entry("2 5|5/3","small stellated truncated dodecahedron", "great pentakisdodekahedron",74,97), /*64*/ new Entry("5/3 2 5|","truncated dodecadodecahedron", "medial disdyakistriacontahedron",75,98), /*65*/ new Entry("|5/3 2 5","inverted snub dodecadodecahedron", "medial inverted pentagonal hexecontahedron",76,114), /* (5/3 5/2 3) (I10a) */ /*66*/ new Entry("5/2 3|5/3","great dodecicosidodecahedron", "great dodecacronic hexecontahedron",77,99), /*67*/ new Entry("5/3 5/2|3","small dodecahemicosahedron", "small dodecahemicosacron",78,100), /*68*/ new Entry("5/3 5/2 3|","great dodecicosahedron", "great dodecicosacron",79,101), /*69*/ new Entry("|5/3 5/2 3","great snub dodecicosidodecahedron", "great hexagonal hexecontahedron",80,115), /* (5/4 3 5) (I10b) */ /*70*/ new Entry("5/4 5|3","great dodecahemicosahedron", "great dodecahemicosacron",81,102), /* (5/3 2 3) (I13) */ /*71*/ new Entry("2 3|5/3","great stellated truncated dodecahedron", "great triakisicosahedron",83,104), /*72*/ new Entry("5/3 3|2","great rhombicosidodecahedron", "great deltoidal hexecontahedron",84,105), /*73*/ new Entry("5/3 2 3|","great truncated icosidodecahedron", "great disdyakistriacontahedron",87,108), /*74*/ new Entry("|5/3 2 3","great inverted snub icosidodecahedron", "great inverted pentagonal hexecontahedron",88,116), /* (5/3 5/3 5/2) (I18a) */ /*75*/ new Entry("5/3 5/2|5/3","great dodecahemidodecahedron", "great dodecahemidodecacron",86,107), /* (3/2 5/3 3) (I18b) */ /*76*/ new Entry("3/2 3|5/3","great icosihemidodecahedron", "great icosihemidodecacron",85,106), /* (3/2 3/2 5/3) (I22) */ /*77*/ new Entry("|3/2 3/2 5/2","small retrosnub icosicosidodecahedron", "small hexagrammic hexecontahedron",91,118), /* (3/2 5/3 2) (I23) */ /*78*/ new Entry("3/2 5/3 2|","great rhombidodecahedron", "great rhombidodecacron",89,109), /*79*/ new Entry("|3/2 5/3 2","great retrosnub icosidodecahedron", "great pentagrammic hexecontahedron",90,117), /****************************************************************************** * Last But Not Least ******************************************************************************/ /*80*/ new Entry("3/2 5/3 3 5/2","great dirhombicosidodecahedron", "great dirhombicosidodecacron",92,119) }; public static class Entry { public final String wythoff; public final String name; public final String dual; public final int coxeter; public final int wenninger; private Entry(String wythoff, String name, String dual, int coxeter, int wenninger) { this.wythoff = wythoff; this.name = name; this.dual = dual; this.coxeter = coxeter; this.wenninger = wenninger; } } }