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91 publications using GAP in the category "Convex and discrete geometry"[ABL17] Adiprasito, K. A., Benedetti, B., and Lutz, F. H., Extremal examples of collapsible complexes and random discrete Morse theory, Discrete Comput. Geom., 57 (4) (2017), 824–853. [AGL14] Akiyama, S., Gähler, F., and Lee, J., Determining pure discrete spectrum for some selfaffine tilings, Discrete Math. Theor. Comput. Sci., 16 (3) (2014), 305–316. [AC+05] Artal Bartolo, E., Carmona Ruber, J., CogolludoAgustín, J. I., and Marco Buzunáriz, M., Topology and combinatorics of real line arrangements, Compos. Math., 141 (6) (2005), 1578–1588. [BD12] Bagchi, B. and Datta, B., A triangulation of $\Bbb CP^3$ as symmetric cube of $S^2$, Discrete Comput. Geom., 48 (2) (2012), 310–329. [B99] Bailey, G. D., Coherence and enumeration of tilings of $3$zonotopes, Discrete Comput. Geom., 22 (1) (1999), 119–147. [BB+09] Ballinger, B., Blekherman, G., Cohn, H., Giansiracusa, N., Kelly, E., and Schürmann, A., Experimental study of energyminimizing point configurations on spheres, Experiment. Math., 18 (3) (2009), 257–283. [BC12] Barakat, M. and Cuntz, M., Coxeter and crystallographic arrangements are inductively free, Adv. Math., 229 (1) (2012), 691–709. [BH+09] Baumeister, B., Haase, C., Nill, B., and Paffenholz, A., On permutation polytopes, Adv. Math., 222 (2) (2009), 431–452. [BM+14] Berman, L. W., Mixer, M., Monson, B., Oliveros, D., and Williams, G., The monodromy group of the $n$pyramid, Discrete Math., 320 (2014), 55–63. [BM+15] Berman, L. W., Monson, B., Oliveros, D., and Williams, G. I., The monodromy group of a truncated simplex, J. Algebraic Combin., 42 (3) (2015), 745–761. [BD+13] Bishop, M., Douglass, J. M., Pfeiffer, G., and Röhrle, G., Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six, J. Algebra, 377 (2013), 320–332. [BD+15] Bishop, M., Douglass, J. M., Pfeiffer, G., and Röhrle, G., Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight, J. Algebra, 423 (2015), 1213–1232. [BG+96] Bokowski, J., Guedes de Oliviera, A., Thiemann, U., and Veloso da Costa, A., On the cube problem of Las Vergnas, Geom. Dedicata, 63 (1) (1996), 25–43. [BD+14] Bremner, D., Dutour Sikirić, M., Pasechnik, D. V., Rehn, T., and Schürmann, A., Computing symmetry groups of polyhedra, LMS J. Comput. Math., 17 (1) (2014), 565–581. [CT16] Caroli, M. and Teillaud, M., Delaunay triangulations of closed Euclidean $d$orbifolds, Discrete Comput. Geom., 55 (4) (2016), 827–853. [C05] Cochet, C., Kostka numbers and LittlewoodRichardson coefficients, in Integer points in polyhedra—geometry, number theory, algebra, optimization, Amer. Math. Soc., Providence, RI, Contemp. Math., 374 (2005), 79–89.
[C02] Cousineau, G.,
Tilings as a programming exercise,
Theoret. Comput. Sci.,
281 (12)
(2002),
207–217 [C12] Cunningham, G., Mixing chiral polytopes, J. Algebraic Combin., 36 (2) (2012), 263–277. [C12] Cunningham, G., Mixing regular convex polytopes, Discrete Math., 312 (4) (2012), 763–771. [CP14] Cunningham, G. and Pellicer, D., Chiral extensions of chiral polytopes, Discrete Math., 330 (2014), 51–60. [DLM10] Dai Pra, P., Louis, P., and Minelli, I. G., Realizable monotonicity for continuoustime Markov processes, Stochastic Process. Appl., 120 (6) (2010), 959–982. [DS13] Datta, B. and Singh, N., An infinite family of tight triangulations of manifolds, J. Combin. Theory Ser. A, 120 (8) (2013), 2148–2163. [DJS11] D'Azevedo, A. B., Jones, G. A., and Schulte, E., Constructions of chiral polytopes of small rank, Canad. J. Math., 63 (6) (2011), 1254–1283.
[DH00] Delgado Friedrichs, O. and Huson, D. H.,
4regular vertextransitive tilings of $\bold E^3$,
Discrete Comput. Geom.,
24 (23)
(2000),
279–292 [DH99] Delgado Friedrichs, O. and Huson, D. H., Tiling space by Platonic solids. I, Discrete Comput. Geom., 21 (2) (1999), 299–315. [DEJ14] Derenthal, U., Elsenhans, A., and Jahnel, J., On the factor alpha in Peyre's constant, Math. Comp., 83 (286) (2014), 965–977. [DM12] DontenBury, M. and Michałek, M., Phylogenetic invariants for groupbased models, J. Algebr. Stat., 3 (1) (2012), 44–63. [DFM04] Dougherty, R., Faber, V., and Murphy, M., Unflippable tetrahedral complexes, Discrete Comput. Geom., 32 (3) (2004), 309–315. [D04] Dutour, M., The sixdimensional Delaunay polytopes, European J. Combin., 25 (4) (2004), 535–548. [DD04] Dutour, M. and Deza, M., GoldbergCoxeter construction for 3 and 4valent plane graphs, Electron. J. Combin., 11 (1) (2004), Research Paper 20, 49. [DER07] Dutour, M., Erdahl, R., and Rybnikov, K., Perfect Delaunay polytopes in low dimensions, Integers, 7 (2007), A39, 49. [D17] Dutour Sikirić, M., The seven dimensional perfect Delaunay polytopes and Delaunay simplices, Canad. J. Math., 69 (5) (2017), 1143–1168. [DIP07] Dutour Sikirić, M., Itoh, Y., and Poyarkov, A., Cube packings, second moment and holes, European J. Combin., 28 (3) (2007), 715–725. [DSV10] Dutour Sikirić, M., Schürmann, A., and Vallentin, F., The contact polytope of the Leech lattice, Discrete Comput. Geom., 44 (4) (2010), 904–911. [E09] Edmonds, A. L., The partition problem for equifacetal simplices, Beiträge Algebra Geom., 50 (1) (2009), 195–213. [E11] Effenberger, F., Stacked polytopes and tight triangulations of manifolds, J. Combin. Theory Ser. A, 118 (6) (2011), 1843–1862. [EK10] Effenberger, F. and Kühnel, W., Hamiltonian submanifolds of regular polytopes, Discrete Comput. Geom., 43 (2) (2010), 242–262. [FL16] Friese, E. and Ladisch, F., Affine symmetries of orbit polytopes, Adv. Math., 288 (2016), 386–425. [GTV03] Garber, D., Teicher, M., and Vishne, U., $\pi_1$classification of real arrangements with up to eight lines, Topology, 42 (1) (2003), 265–289. [GHK13] Gähler, F., Hunton, J., and Kellendonk, J., Integral cohomology of rational projection method patterns, Algebr. Geom. Topol., 13 (3) (2013), 1661–1708. [GLD18] Gomi, Y., Loyola, M. L., and De Las Peñas, M. L. A. N., String Cgroups of order 1024, Contrib. Discrete Math., 13 (1) (2018), 1–22. [G11] Gonçalves, D., On the $K$theory of the stable $C^*$algebras from substitution tilings, J. Funct. Anal., 260 (4) (2011), 998–1019. [H11] Hartley, M. I., Eulerian abstract polytopes, Aequationes Math., 82 (12) (2011), 1–23. [H06] Hartley, M. I., Simpler tests for semisparse subgroups, Ann. Comb., 10 (3) (2006), 343–352. [H03] Hartley, M. I., Quotients of some finite universal locally projective polytopes, Discrete Comput. Geom., 29 (3) (2003), 435–443. [H05] Hartley, M. I., Locally projective polytopes of type $\4,3,\dots,3,p\$, J. Algebra, 290 (2) (2005), 322–336. [H08] Hartley, M. I., An exploration of locally projective polytopes, Combinatorica, 28 (3) (2008), 299–314. [H10] Hartley, M. I., Covers $\scr P$ for abstract regular polytopes $\scr Q$ such that $\scr Q=\scr P/\bf Z^k_p$, Discrete Comput. Geom., 44 (4) (2010), 844–859. [H06] Hartley, M. I., An atlas of small regular abstract polytopes, Period. Math. Hungar., 53 (12) (2006), 149–156. [HH10] Hartley, M. I. and Hulpke, A., Polytopes derived from sporadic simple groups, Contrib. Discrete Math., 5 (2) (2010), 106–118. [HL04] Hartley, M. I. and Leemans, D., Quotients of a universal locally projective polytope of type $\5,3,5\$, Math. Z., 247 (4) (2004), 663–674. [HL09] Hartley, M. I. and Leemans, D., On locally spherical polytopes of type $\5,3,5\$, Discrete Math., 309 (1) (2009), 247–254. [HMS00] Hausel, T., Makai Jr. , E., and Szűcs, A., Inscribing cubes and covering by rhombic dodecahedra via equivariant topology, Mathematika, 47 (12) (2000), 371–397 (2002). [HRS15] Herr, K., Rehn, T., and Schürmann, A., On latticefree orbit polytopes, Discrete Comput. Geom., 53 (1) (2015), 144–172. [HJ+09] Herrmann, S., Jensen, A., Joswig, M., and Sturmfels, B., How to draw tropical planes, Electron. J. Combin., 16 (2, Special volume in honor of Anders Björner) (2009), Research Paper 6, 26. [HR16] Hoge, T. and Röhrle, G., Nice reflection arrangements, Electron. J. Combin., 23 (2) (2016), Paper 2.9, 24. [HL07] Hohlweg, C. and Lange, C. E. M. C., Realizations of the associahedron and cyclohedron, Discrete Comput. Geom., 37 (4) (2007), 517–543. [HP04] Hood, J. and Perkinson, D., Some facets of the polytope of even permutation matrices, Linear Algebra Appl., 381 (2004), 237–244.
[KL99] Kühnel, W. and Lutz, F. H.,
A census of tight triangulations,
Period. Math. Hungar.,
39 (13)
(1999),
161–183 [KK03] Kimmerle, W. and Kouzoudi, E., Doubly transitive automorphism groups of combinatorial surfaces, Discrete Comput. Geom., 29 (3) (2003), 445–457. [L16] Ladisch, F., Realizations of abstract regular polytopes from a representation theoretic view, Aequationes Math., 90 (6) (2016), 1169–1193.
[LST01] Lempken, W., Schröder, B., and Tiep, P. H.,
Symmetric squares, spherical designs, and lattice minima,
J. Algebra,
240 (1)
(2001),
185–208 [L08] Long, C., Small volume closed hyperbolic 4manifolds, Bull. Lond. Math. Soc., 40 (5) (2008), 913–916.
[L99] Lutz, F. H.,
Triangulated manifolds with few vertices and vertextransitive group actions,
Verlag Shaker, Aachen,
Berichte aus der Mathematik. [Reports from Mathematics]
(1999),
vi+137 pages
[L02] Lutz, F. H.,
Examples of $\Bbb Z$acyclic and contractible vertexhomogeneous simplicial
complexes,
Discrete Comput. Geom.,
27 (1)
(2002),
137–154 [L08] Lutz, F. H., Combinatorial 3manifolds with 10 vertices, Beiträge Algebra Geom., 49 (1) (2008), 97–106. [M09] Marco Buzunáriz, M. Á., A description of the resonance variety of a line combinatorics via combinatorial pencils, Graphs Combin., 25 (4) (2009), 469–488. [M14] McMullen, P., Realizations of regular polytopes, IV, Aequationes Math., 87 (12) (2014), 1–30. [MPW14] Monson, B., Pellicer, D., and Williams, G., Mixing and monodromy of abstract polytopes, Trans. Amer. Math. Soc., 366 (5) (2014), 2651–2681. [MPW12] Monson, B., Pellicer, D., and Williams, G., The tomotope, Ars Math. Contemp., 5 (2) (2012), 355–370. [MP+07] Monson, B., Pisanski, T., Schulte, E., and Weiss, A. I., Semisymmetric graphs from polytopes, J. Combin. Theory Ser. A, 114 (3) (2007), 421–435. [MS10] Monson, B. and Schulte, E., Locally toroidal polytopes and modular linear groups, Discrete Math., 310 (12) (2010), 1759–1771. [MS14] Monson, B. and Schulte, E., Finite polytopes have finite regular covers, J. Algebraic Combin., 40 (1) (2014), 75–82. [MS04] Monson, B. and Schulte, E., Reflection groups and polytopes over finite fields. I, Adv. in Appl. Math., 33 (2) (2004), 290–317. [MS07] Monson, B. and Schulte, E., Reflection groups and polytopes over finite fields. II, Adv. in Appl. Math., 38 (3) (2007), 327–356. [MS12] Monson, B. and Schulte, E., Semiregular polytopes and amalgamated Cgroups, Adv. Math., 229 (5) (2012), 2767–2791. [MW07] Monson, B. and Weiss, A. I., Medial layer graphs of equivelar 4polytopes, European J. Combin., 28 (1) (2007), 43–60. [P17] Pasechnik, D. V., Locally toroidal polytopes of rank 6 and sporadic groups, Adv. Math., 312 (2017), 459–472. [P10] Pellicer, D., A construction of higher rank chiral polytopes, Discrete Math., 310 (67) (2010), 1222–1237. [P14] Pellicer, D., Vertextransitive maps with Schläfli type $\3,7\$, Discrete Math., 317 (2014), 53–74. [PB14] Plesken, W. and Bächler, T., Counting polynomials for linear codes, hyperplane arrangements, and matroids, Doc. Math., 19 (2014), 285–312. [R03] Reid, M., Tile homotopy groups, Enseign. Math. (2), 49 (12) (2003), 123–155. [S10] Schürmann, A., Perfect, strongly eutactic lattices are periodic extreme, Adv. Math., 225 (5) (2010), 2546–2564. [S11] Spreer, J., Normal surfaces as combinatorial slicings, Discrete Math., 311 (14) (2011), 1295–1309. [S12] Spreer, J., Partitioning the triangles of the cross polytope into surfaces, Beitr. Algebra Geom., 53 (2) (2012), 473–486. [SK11] Spreer, J. and Kühnel, W., Combinatorial properties of the $K3$ surface: simplicial blowups and slicings, Exp. Math., 20 (2) (2011), 201–216. [S01] Suciu, A. I., Fundamental groups of line arrangements: enumerative aspects, in Advances in algebraic geometry motivated by physics (Lowell, MA, 2000), Amer. Math. Soc., Providence, RI, Contemp. Math., 276 (2001), 43–79.
[S02] Suciu, A. I.,
Translated tori in the characteristic varieties of complex hyperplane arrangements,
Topology Appl.,
118 (12)
(2002),
209–223 [T08] Timofeenko, A. V., NonPlatonic and nonArchimedean noncomposite polyhedra, Fundam. Prikl. Mat., 14 (2) (2008), 179–205. [UTM14] Upadhyay, A. K., Tiwari, A. K., and Maity, D., Semiequivelar maps, Beitr. Algebra Geom., 55 (1) (2014), 229–242. [WB04] Wilson, S. and Breda d'Azevedo, A., Surfaces having no regular hypermaps, Discrete Math., 277 (13) (2004), 241–274. 
The GAP Group Last updated: Thu Jun 7 12:15:03 2018 