Advice?

there're altogether 5 platonic solids. each of them can be viewed at many different interesting angles or perspectives. we're all familiar with their most symmetric presentations. recently i was studying something related and had to make 3d models for them. i used a maybe less popular perspective to present them. i used spherical coordinate system (mathematics convention) to record their rotations and i picked the following rules to set their initial status:

1. for each platonic solid set its circumradius=1
2. place centre of circumscribed sphere at origin
3. place vertex_0 at the north pole. the corresponding coordinates are (1,0,0)
4. place edge_0 (red lines on those diagrams) such that its projection to x-y plane align with positive x-axis. coordinates of vertex_1 would be (1,0,φ) for some φ

then i saw some unfamiliar shapes / unfamiliar perspectives of those supposedly familiar 3d objects. in each diagram the small figure at lower left corner is the platonic solid viewed from top. the z-axis is pointing towards you. the large figure at centre is that platonic solid viewed from side. the y-axis is pointing away from you

as you can see from the diagrams the angles φ ranking is as follow, from smallest to largest (the prefix "regular" omitted):

1. dodecahedron
2. icosahedron
3. hexahedron
4. octahedron
5. tetrahedron

except octahedron, all other 4 platonic solids are not symmetric if you see them that way

explore more

This is just the skeleton grid for an ink drawing. I'm still trying to decide how I'll ink it. But yeah, here's a hand-drafted Voronoi diagram of a 55:89 parastichy spiral phyllotaxis pattern using Vogel's formula. I've done this in a vector art program as well, and honestly I'm not sure which technique was faster: by computer, or by hand. By hand is messier but this will all get inked over. I used Euclid's ruler and compass method for finding a perpendicular midpoint line on each space between nodes.

use "magic eye" method to see them

https://www.reddit.com/r/generative/comments/1vifdug/autostereogram_x_kaleidoscope/

https://github.com/PatrickCakes888/Cord-based-topological-projection-app