There is an increasingly extensive literature on the problem of describing the connection (monodromy) groups and automorphism groups of families of polytopes and maniplexes that are not regular or reflexible. Many such polytopes and maniplexes arise as the result of constructions such as truncations and products. Here we show that for a wide variety of these constructions, the connection group of the output can be described in a nice way in terms of the connection group of the input. We call such operations stratified. Moreover, we show that, if $F$ is a maniplex operation in one of two broad subclasses of stratified operations, and if $\mathcal{R}$ is the smallest reflexible cover of some maniplex $\mathcal{M}$, then the connection group of $F\left(\mathcal{R}\right)$ is equal to the connection group of $F\left(\mathcal{M}\right)$. In particular, we show that this is true for truncations and medials of maps, for products of polytopes (including pyramids and prisms over polytopes), and for the mix of maniplexes. As an application, we determine the smallest reflexible covers of the pyramids over the equivelar toroidal maps.

Revised:

Accepted:

Published online:

Keywords: Polytope, maniplex, connection group, monodromy group, truncation, medial, pyramid, prism

^{1}; Pellicer, Daniel

^{2}; Williams, Gordon

^{3}

@article{ALCO_2022__5_2_267_0, author = {Cunningham, Gabe and Pellicer, Daniel and Williams, Gordon}, title = {Stratified operations on maniplexes}, journal = {Algebraic Combinatorics}, pages = {267--287}, publisher = {The Combinatorics Consortium}, volume = {5}, number = {2}, year = {2022}, doi = {10.5802/alco.208}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/alco.208/} }

TY - JOUR AU - Cunningham, Gabe AU - Pellicer, Daniel AU - Williams, Gordon TI - Stratified operations on maniplexes JO - Algebraic Combinatorics PY - 2022 SP - 267 EP - 287 VL - 5 IS - 2 PB - The Combinatorics Consortium UR - http://archive.numdam.org/articles/10.5802/alco.208/ DO - 10.5802/alco.208 LA - en ID - ALCO_2022__5_2_267_0 ER -

%0 Journal Article %A Cunningham, Gabe %A Pellicer, Daniel %A Williams, Gordon %T Stratified operations on maniplexes %J Algebraic Combinatorics %D 2022 %P 267-287 %V 5 %N 2 %I The Combinatorics Consortium %U http://archive.numdam.org/articles/10.5802/alco.208/ %R 10.5802/alco.208 %G en %F ALCO_2022__5_2_267_0

Cunningham, Gabe; Pellicer, Daniel; Williams, Gordon. Stratified operations on maniplexes. Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 267-287. doi : 10.5802/alco.208. http://archive.numdam.org/articles/10.5802/alco.208/

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