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new images generated by my previous program: these are all truncated versions of the 6 regular polychora in 4d Euclidean space: 5-cell, hypercube, 16-cell, 24-cell,120-cell, 600-cell.

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2018/8/12

15 Photos - View album

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A cantitruncated and a runcitruncated 120-cell.

2018/7/12

2 Photos - View album

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I have uploaded the code to github

https://github.com/neozhaoliang/pywonderland

and here are some quick examples I rendered last night with the code. This is an "almost complete" list of what this program currently can do.

It can render all platonic and archimedean solids, all kinds of prisms/duoprisms/antiprisms, all kinds of regular/truncated 4d polytopes like hypercube, 120-cell and 600-cell.

The program is motivated by Jenn3d but now it has gone a lot further than Jenn3d.

One advantage of the approach of computing the symmetry group is that, one can exactly select which vertex/edge/face to show and control its appearance.

Stellated shapes needs to be added in the future.

https://github.com/neozhaoliang/pywonderland

and here are some quick examples I rendered last night with the code. This is an "almost complete" list of what this program currently can do.

It can render all platonic and archimedean solids, all kinds of prisms/duoprisms/antiprisms, all kinds of regular/truncated 4d polytopes like hypercube, 120-cell and 600-cell.

The program is motivated by Jenn3d but now it has gone a lot further than Jenn3d.

One advantage of the approach of computing the symmetry group is that, one can exactly select which vertex/edge/face to show and control its appearance.

Stellated shapes needs to be added in the future.

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2018/7/11

10 Photos - View album

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The snub-dodecahedron and snub-cube (slightly deformed): the math is simple, but finding the right symmetry group and orbit-stabilizers is not.

2018/7/11

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I finally managed to compute the data of all kinds of truncated 3D and 4D polytopes using Todd-Coxeter's approach, and here is one example (I don't remember its name): Coxeter diagram: 5-3-3 (same with 120-cell) and active mirrors are (1110), edges and faces are colored by the reflection / rotation that generate them:

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Wythoff construction of the list of Archimedean solids as in

https://en.wikipedia.org/wiki/Archimedean_solid

Computed in python and exported to POV-Ray. The edges and faces are colored by the type of their reflections/rotations.

For a given Coxeter diagram (for example, 5-3-2) and 3 distances between the initial vertex and the 3 mirrors (for example (1.0, 0.5, 0.3)), I computed the total symmetry group and the 3 vertex/edge/face stabilizing subgroups using Todd-Coxeter's procedure (motivated by Jenn3d), and then got all vertices/edges/faces via the orbit-stabilizer theorem.But this approach seems failed for the two exceptional chiral solids: snub dodecahedron and snub cube. Need help!

https://en.wikipedia.org/wiki/Archimedean_solid

Computed in python and exported to POV-Ray. The edges and faces are colored by the type of their reflections/rotations.

For a given Coxeter diagram (for example, 5-3-2) and 3 distances between the initial vertex and the 3 mirrors (for example (1.0, 0.5, 0.3)), I computed the total symmetry group and the 3 vertex/edge/face stabilizing subgroups using Todd-Coxeter's procedure (motivated by Jenn3d), and then got all vertices/edges/faces via the orbit-stabilizer theorem.But this approach seems failed for the two exceptional chiral solids: snub dodecahedron and snub cube. Need help!

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2018/6/26

11 Photos - View album

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This is a short video I made using POV-Ray's animation feature :

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A new 120-cell scene ! Computed in Python using Todd-Coxeter algorithm and then exported to POV-Ray. It's much like the Dimensions video by Jos Leys:

http://www.dimensions-math.org/Dim_E.htm

http://www.dimensions-math.org/Dim_E.htm

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Mobius transformations in hyperbolic uppper space, rendered with +Roice Nelson 's shader code, I tweaked the color functions and added antialiasing and tone mapping features.

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2018/5/3

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Some 4D polytopes by POV-Ray:

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2018/4/21

3 Photos - View album

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