http://researchonline.federation.edu.au/vital/access/manager/Index en-us 5 http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:16185 Wed 24 Aug 2022 13:32:09 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:16191 Wed 24 Aug 2022 11:09:36 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:14393 Wed 07 Apr 2021 14:02:29 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:13924 Wed 07 Apr 2021 14:02:01 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:13772 3 there are two d-polytopes with d- 1 nonsimple vertices, isomorphic (d- 3) -skeleta and nonisomorphic face lattices. In particular, the result (1) is best possible for 4-polytopes. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.]]> Wed 07 Apr 2021 14:01:53 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:13474 Wed 07 Apr 2021 14:01:37 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:5409 Wed 07 Apr 2021 13:45:03 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:5206 Wed 07 Apr 2021 13:44:50 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:4338 Wed 07 Apr 2021 13:43:47 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:3745 Wed 07 Apr 2021 13:34:46 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1636 Wed 07 Apr 2021 13:32:45 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1313 Wed 07 Apr 2021 13:32:21 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:962 Wed 07 Apr 2021 13:31:57 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:722 Wed 07 Apr 2021 13:31:41 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:439 Wed 07 Apr 2021 13:31:21 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:162 ]]> Wed 07 Apr 2021 13:31:00 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:13991 = 0.62d. This confirms a conjecture of Grunbaum, for these values of m. For v = 2d + 1, we solve the same problem when m = 1 or d - 2; the solution was already known for m = d - 1. In all these cases, we give a characterisation of the minimising polytopes. We also show that there are many gaps in the possible number of m-faces: for example, there is no polytope with 80 edges in dimension 10, and a polytope with 407 edges can have dimension at most 23.]]> Tue 15 Aug 2023 14:37:44 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:14666 Tue 15 Aug 2023 14:31:57 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:15716 Tue 08 Feb 2022 09:33:24 AEDT ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:16555 Tue 06 Sep 2022 16:01:47 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:14449 Thu 25 Nov 2021 11:25:51 AEDT ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:17680 Thu 11 May 2023 09:59:13 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:15164 Thu 07 Jul 2022 14:57:54 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:3215 Thu 05 Jan 2023 14:40:42 AEDT ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:16776 Thu 01 Dec 2022 15:55:06 AEDT ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:19319 Mon 20 May 2024 14:03:09 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:17606 Mon 01 May 2023 14:05:23 AEST ]]>