• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Book chapter
  • The immortaluty of Platonic solids
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
May 25, 2026
HSE Scientists Train Neural Network to 'Hear' Faults in Electric Motors
Researchers at the AI and Digital Science Institute of the HSE Faculty of Computer Science have developed a new method—the Signature-Guided Data Augmentation (SGDA) framework—that achieves 99% accuracy in motor fault detection and 86% accuracy in fault classification. The application of this approach can reduce industrial equipment repair costs, minimise downtime, and improve production safety. The study results have been published in Engineering Applications of Artificial Intelligence.
May 25, 2026
'The Humanities Serve as a Conscience'
Maria Mizernaia studies Soviet literature and the history of book publishing. In this interview for the HSE Young Scientists project, she discusses plans to publish a novel about besieged Leningrad, AI-provoked reflections on what it means to be human, and how novels can help satisfy our dopamine hunger.
May 25, 2026
Is It Possible to Predict a Citys Life Based on the Shape of Its Neighbourhoods?
Is it possible to predict, based on the configuration of streets and buildings, where a café will open or where traffic congestion will occur? Participants in the Spatial Analysis and Modelling of Urban Processes research and study group use open data and machine learning to identify universal patterns. Alexander Sheludkov and Eduard Somov discuss the purpose of comparing cities, the need for new forms of urban statistics, and how open data is transforming approaches to urban studies.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

The immortaluty of Platonic solids

P. 248–253.
Busjatskaja I., Monastyrsky M. I.

The paper examines the significance of Platonic Solids in different parts of modern science.

Language: English
Full text
Keywords: symmetryPlatonic solidsfinite groups

In book

Symmetry: Art and Science. Special Issue for the Congress-Festival of ISIS-Symmetry
Athens: The Hellenic Open University, 2013.
Similar publications
On Non-Symmetric Forms of Time-Varying Autocorrelation Function in the Analysis of Cyclostationary Processes
Shevgunov T., , in: 2024 Systems of signals generating and processing in the field of on board communications.: IEEE, 2024. P. 1–5.
The paper is aimed at investigating the difference between different forms of time-varying autocorrelation function (TVACF) used for the quantitative expression of the second-order statistical properties exhibiting by non-stationary random processes. The generalized form of TVACF is proposed where the position of the current time moment can be set by means of additional parameter. The ...
Added: February 25, 2026
On the saturation of subfields of invariants of finite groups
Arzhantsev I., Petravchuk A. P., Mathematical notes 2009 Vol. 86 No. 5 P. 625–628
Every subfield K(φ) of the field of rational fractions K(x_1, . . . , x_n) is contained in a unique maximal subfield of the form K(ψ). The element ψ is said to be generating for the element φ. A subfield of K(x_1, . . . , x_n) is said to be saturated if, together with ...
Added: June 13, 2025
Лингвосинергетика: Quo vadis?
Милостивая А. И., В кн.: Теория и практика коммуникации: Материалы I Международной научно-практической конференции, Тирасполь, Приднестровский государственный университет им. Т. Г. Шевченко, 27-28 февраля 2023 г.: том 1Т. 1.: Тирасполь: [б.и.], 2023. С. 26–36.
This article analyzes modern linguistic synergetics’ concepts to identify this discipline's main ways and prospects in scientific episteme. The author focuses on the paradigm status and explanatory potential of lingua-synergetic studies. Data for this investigation consists of scientific articles, dissertations and monographs, which set out various versions of the synergistic interpretation of speech activity.  As ...
Added: February 11, 2024
Finite groups of birational transformations
Prokhorov Y., , in: 8th European Congress of Mathematics, Portorož, 20–26 June, 2021.: [б.и.], 2023. P. 413–437.
We survey new results on finite groups of birational transformations of algebraic varieties. ...
Added: November 13, 2023
Отцы и дети, потомки и пращуры. Эволюционное измерение справедливости
Анисимов В. А., МЕТОД: Московский ежегодник трудов из обществоведческих дисциплин 2021 № 11 С. 286–298
This article provides an overview of the theoretical foundations of intergenerational justice. It is shown that the theory of intergenerational justice has two foundations: a symmetric and an asymmetric approach. It also includes the positions of John Rawls and his symmetric concept of justice; Terence Ball and his idea of radical asymmetry; and Ken Binmore ...
Added: June 1, 2022
Finite groups of birational transformations
Prokhorov Y., / Series arXiv "math". 2021.
We survey new results on finite groups of birational transformations of algebraic varieties. ...
Added: November 25, 2021
Derivations of group rings for finite and FC groups
Арутюнов А. А., Kosolapov L., Finite Fields and Their Applications 2021 Vol. 76 Article 101921
In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of ...
Added: October 4, 2021
Finite groups acting on Severi–Brauer surfaces
Shramov K., European Journal of Mathematics 2021 Vol. 7 P. 591–612
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi–Brauer surfaces over fields of characteristic zero. ...
Added: September 8, 2021
Real representations of C2-graded groups: The antilinear theory
Rumynin D., Taylor J., Linear Algebra and its Applications 2021 Vol. 610 P. 135–168
We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite C_2-graded groups. A finite C_2-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial ...
Added: September 7, 2021
КАК ЛЮДИ ИСКУССТВА И НАУКИ ИЗУЧАЮТ ЭТОТ МИР
Оганов А. Р., Konson G., В кн.: Art History in the Context of Other Sciences in Modern World: Parallels and Interaction.: M.: Information and Publishing House Filin, 2020. С. 278–291.
An interview by Grigoriy Konson with Artem R. Oganov, PhD, FRSC MAE, Professor at the Skolkovo Institute of Science and Technology, Professor at the Russian Academy of Sciences, is devoted to crystallography—the science of solid crystalline substances surrounding us, containing an ordered periodic system of atomic positions. Crystallography is at the forefront of the science ...
Added: May 9, 2021
Finite groups acting on Severi-Brauer surfaces
Shramov K., / Series arXiv "math". 2020.
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero. ...
Added: August 19, 2020
Symmetry in large-scale socio-economic systems and the implications for management
Rasskazov, S.V., Rasskazova, A.N., Koroleva, E.V., , in: 2019 Twelfth International Conference "Management of large-scale system development" (MLSD).: M.: IEEE, 2019. P. 1–5.
The paper provides a methodology for identifying and analyzing group-theoretical symmetry in socio-economic applications. Symmetry is disclosed in the tasks of estimating contingent claims, the main hypotheses of financial markets, time series of stock indexes, including pre-crisis periods, the distribution of urban population and the duration of historical periods. The connection of solutions based on ...
Added: January 23, 2020
New Characterization-Based Symmetry Tests
Bozin V., Milošević B., Nikitin Y. Y. et al., Bulletin of the Malaysian Mathematical Sciences Society 2020 Vol. 43 No. 1 P. 297–320
Two new symmetry tests, of integral and Kolmogorov type, based on the characterization by squares of linear statistics are proposed. The test statistics are related to the family of degenerate U-statistics. Their asymptotic properties are explored. The maximal eigenvalue, needed for the derivation of their logarithmic tail behavior, was calculated or approximated using techniques from ...
Added: January 4, 2020
Finite groups acting on elliptic surfaces
Shramov K., / Series arXiv "math". 2019.
We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration. ...
Added: November 19, 2019
Information Security Methods—Modern Research Directions
Шелупанов А. А., Evsyutin O., Конев А. А. et al., Symmetry 2019 Vol. 11 No. 2 P. 1–33
In Tomsk University of Control Systems and Radioelectronics (TUSUR) one of the main areas of research is information security. The work is carried out by a scientific group under the guidance of Professor Shelupanov. One of the directions is the development of a comprehensive approach to assessing the security of the information systems. This direction ...
Added: September 3, 2019
Compressible finite groups of birational automorphisms
Popov V. L., Doklady Mathematics 2018 Vol. 98 No. 2 P. 413–415
The compressibility of certain types of finite groups of birational automorphisms of algebraic varieties is established. ...
Added: November 13, 2018
Tests based on characterizations, and their efficiencies: a survey
Nikitin Y. Y., Acta et Commentationes Universitatis Tartuensis de Mathematica 2017 Vol. 21 No. 1 P. 3–24
A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of U-empirical processes. The limiting distributions and large deviations of new statistics under the null hypothesis are described. Their local Bahadur efficiency for various ...
Added: November 13, 2017
The unreasonable power of the lifting property in elementary mathematics
Gavrilovich M., / Series arxiv "math.CT". 2017.
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing that many standard elementary notions of abstract topology can be defined by applying the lifting property to simple morphisms of ...
Added: July 21, 2017
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit