// SnapPea Triangulation File Format // // This document contains an annotated triangulation file. If you remove // all comments (i.e. remove all text preceded by a double slash) you'll // be left with a SnapPea-readable triangulation file. The manifold is // a (1,1) Dehn filling on one cusp of the Whitehead link complement, which // turns out to be homeomorphic to the figure eight knot complement. // // The information on the hyperbolic structure (solution type, volume, // and tetrahedron shapes) is provided solely for human readers. // The SnapPea kernel ignores this information and recomputes the // hyperbolic structure from scratch. // // The meridian and longitude are optional. The SnapPea kernel will // use them if they are provided. If they are all zero, it will use // a default meridian and longitude. // // The numbers of torus and Klein bottle cusps are also optional. // You may set both to zero (and of course omit the cusp topology // and Dehn filling information) if you want SnapPea to figure out // the cusps for you and assign arbitrary indices. // // 97/12/6 This file format now allows finite ( = non ideal) vertices. // If you have set the number of torus and Klein bottle cusps to zero // (cf. preceding paragraph) SnapPea will figure out for itself which // vertices are ideal and which are finite (by checking the Euler // characteristic of each boundary component). // If you have manually specified the real cusps, then simply assign // an index of -1 for the "incident cusp" of each finite vertex. // Even if there is more than one finite vertex, all get cusp index -1. // // Any low-dimensional topologist should be able to understand the // header information. There is no need to understand the information // about each tetrahedron, but if you want to understand it anyhow you // should first read the file triangulation.h. % Triangulation // Every triangulation file must begin // with the header "% Triangulation". sample // name of manifold geometric_solution 2.02988321 // SolutionType and volume (cf. SnapPea.h) oriented_manifold // Orientability // oriented_manifold // or nonorientable_manifold // or unknown_orientability CS_known 0.00000000000000000000 // CS_known or CS_unknown // if CS_known, value is given 2 0 // number of torus and Klein bottle cusps torus 1.000000000000 1.000000000000 // topology and Dehn filling // for cusp #0 torus 0.000000000000 0.000000000000 // topology and Dehn filling // for cusp #1 // 0 0 means the cusp is unfilled 4 // number of tetrahedra 3 1 2 1 // neighbors (cf. Triangulation.h) 0132 0321 0132 3120 // gluings (in contrast to the old file format, // permutations are given in "forwards order", // e.g. 0123 is the identity) 1 1 0 1 // incident cusps 0 0 0 0 0 0 0 0 0 1 0 -1 -1 1 0 0 // meridian (right sheet) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 // meridian (left sheet) 0 1 0 -1 0 0 -1 1 1 1 0 -2 -1 1 0 0 // longitude (right sheet) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 // longitude (left sheet) 0.429304013127 0.107280447008 // tetrahedron shape // and similarly for the remaining three tetrahedra . . . 0 2 3 0 3120 1230 0132 0321 1 1 0 1 0 0 0 0 0 0 1 -1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 0 2 -1 2 -1 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.692440400998 0.318147957810 3 3 1 0 1023 0213 3012 0132 1 1 1 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 2 -2 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.692440400998 0.318147957810 0 2 2 1 0132 1023 0213 0132 1 1 1 0 0 0 0 0 0 0 1 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -2 1 -2 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.692440400998 0.318147957810