Archimedean and Catalan stellations — twelve selected exterior surfaces Five triakis-tetrahedron layers (TT-L1–TT-L5), three rhombic-dodecahedron layers (RD-L1–RD-L3), and four cuboctahedral stellations (W43–W46). TT-L and RD-L are local, reproducible layer labels, NOT George Hart's model numbers and NOT a claim to include his 21 fully supported triakis-tetrahedron forms. Hart's wider collection remains a useful reference: https://georgehart.com/virtual-polyhedra/stellations-triakis-tetrahedron.html https://georgehart.com/virtual-polyhedra/stellations-info.html The layer construction is original to this explorer. The twelve supporting planes of the exact Catalan parent are retained under data/catalan-stellations/ parents.json. All finite intersections of triples are found, including multiple concurrences. Incident sign cells are enumerated. Linear programming checks a strictly interior point and boundedness in all six coordinate directions. Layer k includes the core and every bounded cell lying outside at most k original supporting half-spaces. TT has levels 0–5; RD has levels 0–3. Shared internal facets are removed. Neighbouring visible regions in each original plane are joined, keeping separate pieces and holes. The outermost layer includes all bounded cells. Intermediate layer names are descriptive; there are many other stellations and other numbering conventions. W43–W46 use Roger Kaufman's original Wenninger diagram selections in Antiprism base/stellations.cc, unchanged at pinned revision: 7805b34d3f8860857fb9ac10a1917d1bf4c7888d https://github.com/antiprism/antiprism https://georgehart.com/virtual-polyhedra/stellations-cuboctahedron.html W43 displays the exterior union of cube and octahedron, hiding their overlap. W44 and W45 are Wenninger's second and third; W46 is the final stellation. These are NOT Hart's six-model numbering. Antiprism source and MIT notices are preserved in data/antiprism/stellations.cc and data/antiprism/COPYING. Its source meshes and original parent are retained under data/catalan-stellations/wenninger-cuboctahedron.json. For all twelve entries, F counts connected planar exterior surface pieces, not complete extended faces. E and V describe their conforming boundary mesh. One parent plane can contain several pieces. Twelve or fourteen original planes are shown separately in properties and comparison. Crossings and occluded interior regions do not add extra faces to this exterior view. Every boundary edge has two incident pieces. The count expression V−E+F is not a general classification of all complete-face stellations. Generate meshes and independent original-facelet coverage references with: python scripts/generate-catalan-stellations.py Offline dependencies: NumPy, SciPy and Shapely. Nothing is fetched at runtime. The exporter scripts/export-catalan-stellations.cc rebuilds W43–W46 from the same pinned Antiprism library used by the other catalogues. Antiprism MIT license: Format: http://www.debian.org/doc/packaging-manuals/copyright-format/1.0/ Upstream-Name: antiprism Upstream-Contact: Adrian Rossiter Source: License: MIT-and-similar permissive with attribution Files: * Comment: Bulk of the files, one author or the other, or both Copyright: 2003-2023, Adrian Rossiter 2006-2023, Roger Kaufman License: Expat Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: . The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. . THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Files: src/canonical* src/conway.cc Comment: Conway notation, Canonicalization Copyright: 2003-2023, Adrian Rossiter 2006-2023, Roger Kaufman License: Expat_plus Includes ideas and algorithms by George W. Hart, http://www.georgehart.com . Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: . The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. . THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Files: base/qhull/* Comment: Qhull - Convex Hulls, Delaunay, Voronoi Copyright: Qhull, Copyright (c) 1993-2003 The National Science and Technology Research Center for Computation and Visualization of Geometric Structures (The Geometry Center) University of Minnesota email: qhull@qhull.org License: Qhull This software includes Qhull from The Geometry Center. Qhull is copyrighted as noted above. Qhull is free software and may be obtained via http from www.qhull.org. It may be freely copied, modified, and redistributed under the following conditions: . 1. All copyright notices must remain intact in all files. . 2. A copy of this text file must be distributed along with any copies of Qhull that you redistribute; this includes copies that you have modified, or copies of programs or other software products that include Qhull. . 3. If you modify Qhull, you must include a notice giving the name of the person performing the modification, the date of modification, and the reason for such modification. . 4. When distributing modified versions of Qhull, or other software products that include Qhull, you must provide notice that the original source code may be obtained as noted above. . 5. There is no warranty or other guarantee of fitness for Qhull, it is provided solely "as is". Bug reports or fixes may be sent to qhull_bug@qhull.org; the authors may or may not act on them as they desire. . ------------------- . Changes from Qhull 2015.2 source made by Adrian Rossiter in Oct 2016 to incorporate Qhull library code into Antiprism: . Only libqhull_r source used. Minor changes made for a clean build as C++. Files: base/getopt.* Comment: Ultra-Getopt Copyright: 2007, Kevin Locke License: Expat Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: . The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. . THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Files: base/random.h Comment: Random number generator Copyright: public domain License: public-domain Robin Whittle rw@firstpr.com.au 2005 September 21 http://www.firstpr.com.au/dsp/rand31/rand31-park-miller-carta.cc.txt Files: base/tesselator/* Comment: GLUtesselator Copyright: 1991-2000 Silicon Graphics, Inc. License: SGI License Applicability. Except to the extent portions of this file are made subject to an alternative license as permitted in the SGI Free Software License B, Version 1.1 (the "License"), the contents of this file are subject only to the provisions of the License. You may not use this file except in compliance with the License. You may obtain a copy of the License at Silicon Graphics, Inc., attn: Legal Services, 1600 Amphitheatre Parkway, Mountain View, CA 94043-1351, or at: . http://oss.sgi.com/projects/FreeB . Note that, as provided in the License, the Software is distributed on an "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A PARTICULAR PURPOSE, AND NON-INFRINGEMENT. . Original Code. The Original Code is: OpenGL Sample Implementation, Version 1.2.1, released January 26, 2000, developed by Silicon Graphics, Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc. Copyright in any portions created by third parties is as indicated elsewhere herein. All Rights Reserved. . Additional Notice Provisions: The application programming interfaces established by SGI in conjunction with the Original Code are The OpenGL(R) Graphics System: A Specification (Version 1.2.1), released April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X Window System(R) (Version 1.3), released October 19, 1998. This software was created using the OpenGL(R) version 1.2.1 Sample Implementation published by SGI, but has not been independently verified as being compliant with the OpenGL(R) version 1.2.1 Specification. Files: base/prop_col.* Comment: Minimal proper colouring (two licences) Copyright: 1994 Michael Trick. 1996-2000 Darko Kirovski, Miodrag Podkonjak and the Regents of the University of California License: Expat_other The author of this software is Michael Trick. Copyright (c) 1994 by Michael Trick. . Permission to use, copy, modify, and distribute this software for any purpose without fee is hereby granted, provided that this entire notice is included in all copies of any software which is or includes a copy or modification of this software and in all copies of the supporting documentation for such software. THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR DOES NOT MAKE ANY REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. . COLOR.C: Easy code for graph coloring Author: Michael A. Trick, Carnegie Mellon University, trick+@cmu.edu Last Modified: November 2, 1994 http://mat.gsia.cmu.edu/COLOR/solvers/trick.c . ------------------------------------------------------------------------ . Contact author(s) for original code: darko@cs.ucla.edu, miodrag@cs.ucla.edu Affiliationss: UCLA, Computer Science . Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: . The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. . THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Files: base/muparser/* Comment: muParser - A fast math parser library Copyright: 2011 Ingo Berg Web: muparser.beltoforion.de e-mail: muparser@beltoforion.de License: Expat Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: . The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. . THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Files: src/tiny_obj_loader.h Comment: helper code to load an obj file to convert to an off file Copyright: 2012-Present, Syoyo Fujita and many contributors. License: Expat Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: . The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. . THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.