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From: Expanding polyhedral universe in Regge calculus

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Presentation on theme: "From: Expanding polyhedral universe in Regge calculus"— Presentation transcript:

1 From: Expanding polyhedral universe in Regge calculus
Fig. 1. The $i$th frustum as the fundamental building block of a polyhedral universe for $p=3$: Each face of the regular polygon with edge length $l_i$ at time $t_i$ expands to the upper one with $l_{i+1} $ at $t_{i+1} $. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

2 From: Expanding polyhedral universe in Regge calculus
Fig. 6. Plots of the dihedral angles of pseudo-regular polyhedral universes for $\nu\leq5$. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

3 From: Expanding polyhedral universe in Regge calculus
Fig. 2. Plots of the dihedral angles of the regular polyhedral models: each plot ends at $t=t_{p,q}$. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

4 From: Expanding polyhedral universe in Regge calculus
Fig. 3. Plots of the scale factors of the regular polyhedral models. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

5 From: Expanding polyhedral universe in Regge calculus
Fig. 4. Subdivision of a regular triangle: sides with distinct alphabetical labels are projected onto edges of different lengths in the geodesic dome. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

6 From: Expanding polyhedral universe in Regge calculus
Fig. 5. Projection of tessellated icosahedrons onto the circumsphere. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

7 From: Expanding polyhedral universe in Regge calculus
Fig. 9. Dihedral angle of the pseudo-regular polyhedron for $\nu=100$. The broken line corresponds to the solution in the infinite frequency limit $\theta_\infty(t)=\pi/3$. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

8 From: Expanding polyhedral universe in Regge calculus
Fig. 7. Plots of the scale factors of pseudo-regular polyhedrons and geodesic domes for $\nu\leq5$. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

9 From: Expanding polyhedral universe in Regge calculus
Fig. 10. Scale factor of the pseudo-regular polyhedron for $\nu=100$. The broken curve is the scale factor of the continuum theory. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

10 From: Expanding polyhedral universe in Regge calculus
Fig. 8. Plots of $|a_\mathrm{R}-a_\mathrm{gd}|/a_\mathrm{gd}$ for $2\leq \nu\leq5$. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

11 From: Expanding polyhedral universe in Regge calculus
Fig. 11. Faces projected onto the sphere. From: Expanding polyhedral universe in Regge calculus Prog Theor Exp Phys. 2017;2017(7). doi: /ptep/ptx103 Prog Theor Exp Phys | © The Author(s) Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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