Geodesic
Minimum number of edges of polytopes with \(2d+2\) vertices
Guillermo Pineda-Villavicencio1 ; Julien Ugon1 ; David Yost2
1Deakin University
2Federation University
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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We define two $d$-polytopes, both with $2d+2$ vertices and $(d+3)(d-1)$ edges, which reduce to the cube and the 5-wedge in dimension three. We show that they are the only minimisers of the number of edges, amongst all $d$-polytopes with $2d+2$ vertices, when $d=6$ or $d\ge8$. We also characterise the minimising polytopes for $d=4, 5$ or 7, where four sporadic examples arise.
DOI : 10.37236/10374
Classification : 52B05, 52B12
Mots-clés : minimisers of the number of edges, \(d\)-polytopes with \(2d+2\) vertices

Guillermo Pineda-Villavicencio  1   ; Julien Ugon  1   ; David Yost  2

1 Deakin University
2 Federation University 
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     title = {Minimum number of edges of polytopes with \(2d+2\) vertices},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
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Guillermo Pineda-Villavicencio; Julien Ugon; David Yost. Minimum number of edges of polytopes with \(2d+2\) vertices. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10374

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