Dong-Dong Hou

activity

20182026

2^{n}

3 citations · 5 across the 10 of their papers we have counts for

collaborators

10 papers

math.GR2026

String C-groups of 2-power order project onto a common string C-group

Dong-Dong Hou, Egon Schulte

String C-groups are precisely the automorphism groups of abstract regular polytopes. A certain regular d-polytope C_d with an automorphism group of order 2^{2d-1}, discovered by Co…

math.GR2025

Symmetric polytopes whose automorphism groups are 2-groups

Gabriel Cunningham, Yan-Quan Feng, Dong-Dong Hou +1

The present work investigates regular, semiregular, and chiral polytopes of any rank $d \geq 3$ , whose automorphism groups are 2-groups. There is a large variety of rather small fin…

math.GR2025

Chiral polytopes of order $2 p^{m}$

Ting-Ting Kong, Yan-Quan Feng, Dong-Dong Hou +2

Let $P$ be a chiral polytope with type ${k_{1}, k_{2}}$ and $G = A u t (P)$ . Suppose $∣ G ∣ = 2 p^{m}$ , where $k_{1}, k_{2} \geq 3$ and $p$ is an odd prime. Let $P$ be a Sylow $p$ …

math.GR2024

String C-groups of order $4 p^{m}$

Dong-Dong Hou, Yan-Quan Feng, Dimitri Leemans +1

Let $(G, {ρ_{0}, ρ_{1}, ρ_{2}})$ be a string C-group of order $4 p^{m}$ with type ${k_{1}, k_{2}}$ for $m \geq 2$ , $k_{1}, k_{2} \geq 3$ and $p$ be an odd prime. Let $P$ be a Sylow $p$ -subgroup o…

math.CO2021

A family of regular polytopes of order $4 p^{m}$ with type ${p, 2 p}$

Dong-Dong Hou, Ting-Ting Kong, Hai-Peng Qu

In this paper, we construct an infinite families of group $G$ of order $4 p^{m}$ which can be an automorphism group of some regular polytope with type ${p, 2 p}$ , where $m \geq 3$ an…

math.CO2020★ 1 cited

Regular $3$ -polytopes of order $2^{n} p$

Dong-Dong Hou, Yan-Quan Feng, Dimitri Leemans

In [Problems on polytopes, their groups, and realizations, Periodica Math. Hungarica 53 (2006) 231-255] Schulte and Weiss proposed the following problem: {\em Characterize regular…

math.CO2019★ 1 cited

Existence of regular $3$ -hypertopes with $2^{n}$ chambers

Dong-Dong Hou, Yan-Quan Feng, Dimitri Leemans

For any positive integers $n, s, t, l$ such that $n \geq 10$ , $s, t \geq 2$ , $l \geq 1$ and $n \geq s + t + l$ , a new infinite family of regular 3-hypertopes with type $(2^s, 2^t, 2^l)…

math.GR2019★ 3 cited

On regular polytopes of order $2^{n}$

Dong-Dong Hou, Yanquan Feng, Dimitri Leemans

For each $d \geq 3$ , $n \geq 10$ , and $k_{1}, k_{2}, \dots, k_{d - 1} \geq 2$ with $k_{1} + k_{2} + \dots + k_{d - 1} \leq n - 1$ , we construct a regular $d$ -polytope whose automorphism group is of ord…

math.CO2019

Regular maps of order $2$ -powers

Dong-Dong Hou, Yan-Quan Feng, Young Soo Kwon

In this paper, we consider the possible types of regular maps of order $2^{n}$ , where the order of a regular map is the order of automorphism group of the map. For $n \leq 11$ , M. Con…

math.CO2018

$2$ -groups behaving as automorphism groups of regular $3$ -polytopes

Dong-Dong Hou, Yan-Quan Feng, Dimitri Leemans

In this paper, we classify regular polytopes with automorphism groups of order $2^{n}$ and Schläfli types ${4, 2^{n - 3}}, {4, 2^{n - 4}}$ and ${4, 2^{n - 5}}$ for $n \geq 10$ , there…

String C-groups of 2-power order project onto a common string C-group

Symmetric polytopes whose automorphism groups are 2-groups

Chiral polytopes of order 2pm

String C-groups of order 4pm

A family of regular polytopes of order 4pm with type {p,2p}

Regular 3-polytopes of order 2np

Existence of regular 3-hypertopes with 2n chambers

On regular polytopes of order 2n

Regular maps of order 2-powers

2-groups behaving as automorphism groups of regular 3-polytopes

Chiral polytopes of order $2 p^{m}$

String C-groups of order $4 p^{m}$

A family of regular polytopes of order $4 p^{m}$ with type ${p, 2 p}$

Regular $3$ -polytopes of order $2^{n} p$

Existence of regular $3$ -hypertopes with $2^{n}$ chambers

On regular polytopes of order $2^{n}$

Regular maps of order $2$ -powers

$2$ -groups behaving as automorphism groups of regular $3$ -polytopes