https://doi.org/10.1140/epjc/s10052-025-15016-w
Regular Article - Theoretical Physics
Quantum spacetime imprints: the 24-cell, Standard Model symmetry and its flavor mixing
1
Essex County College, 303 University Ave, 07102, Newark, NJ, USA
2
Department of Physics, Faculty of Science, Benha University, 13518, Benha, Egypt
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
12
June
2025
Accepted:
31
October
2025
Published online:
11
November
2025
In our previous work (Ali, Fortsch. Phys. 72(4), 2200210 (2024)), We outline an exploratory framework in which in which the 24-cell acts both as the quantum of spacetime and as a geometric representation of elementary particles. In this paper, we provide comprehensive mathematical and phenomenological evidence that deepens and refines this primary model. The remarkable symmetry of the 24-cell naturally yields a unified hypercharge functional that reproduces the observed Standard Model hypercharge assignments while ensuring anomaly cancellation. By projecting the 24-cell’s vertices onto a three-dimensional flavor subspace using a Minimal Distortion Principle, an emergent tetrahedral structure is revealed that gives rise to an effective 
symmetry in the neutrino sector. Moreover, extending this discrete symmetry to its binary double cover 
supplies the spinorial representations and intrinsic complex phases necessary for generating realistic quark Yukawa textures. Guided by the fundamental tenet that spacetime and matter are inextricably linked, our analysis shows that the intricate flavor mixing of the Standard Model may well be a residual imprint of the underlying quantum-geometric nature of spacetime.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
