Surface Edge Filled Surface

The above surfaces were constructed from spherical projections of the Platonic Solid Edges example, hence the similarity of the Figure 1 script.

The following figure was constructed from cylindrical projections of the surface edges shown in the Base Class Surface 2 and Base Class Geometric Mapping examples.

For all these cases, ‘inner’ or ‘outer’ surface planes are shown. For this reason, shading included the argument ax=ax.

import numpy as np
import matplotlib.pyplot as plt
import s3dlib.surface as s3d

#.. Platonic Solid Surface Edges Filled

# Figure 1 ================================================================

radial_Color = lambda c : s3d.SphericalSurface.coor_convert(c)[0] 

surfaceType = ['tetra','octa','icosa','','cube','dodeca']

fig = plt.figure()
minmax = (-.67,.67)  
for i,stgID in enumerate(surfaceType) :   
    ax =  fig.add_subplot(231+i, projection='3d', aspect='equal')
    ax.set(xlim=(-1, 1), ylim=(-1, 1), zlim=(-1, 1))
    ax.set_axis_off()
    ax.set(xlim=minmax, ylim=minmax, zlim=minmax)
    if len(stgID) == 0 : continue
    surface = s3d.SphericalSurface.platonic(0,stgID)
    line = surface.edges
    surface = line.get_filled_surface(coor='s',dist=0.01, lrez=5,name=stgID)
    surface.map_cmap_from_op( radial_Color,'rainbow_r' )
    ax.set_title(surface.name, fontsize='x-large')
    ax.set_proj_type('ortho')
    ax.view_init(20,-15)

    ax.add_collection3d(surface.shade(0.4,ax=ax))

fig.tight_layout()

# Figure 2 ================================================================

radial_Color_cyl = lambda c : s3d.CylindricalSurface.coor_convert(c)[0] 

verts,R,H = [None]*17 , np.cos(np.pi/5),np.sin(np.pi/5)
for i in range(0,5) :
    verts[i] = [np.cos(2*i*np.pi/5),np.sin(2*i*np.pi/5),0.0]
for i in range(5,10) :
    verts[i]   = [R*np.cos((1+2*i)*np.pi/5),R*np.sin((1+2*i)*np.pi/5), H]
    verts[i+5] = [R*np.cos((1+2*i)*np.pi/5),R*np.sin((1+2*i)*np.pi/5),-H]
verts[15] = [0.0,0.0, 1/H]
verts[16] = [0.0,0.0,-1/H]

faceIndices_4  = [
    [15, 5, 1, 6], [15, 6, 2, 7], [15, 7, 3, 8], [15, 8, 4, 9], [15, 9, 0, 5],
    [ 5, 0,10, 1], [ 6, 1,11, 2], [ 7, 2,12, 3], [ 8, 3,13, 4], [ 9, 4,14, 0],
    [16,11, 1,10], [16,12, 2,11], [16,13, 3,12], [16,14, 4,13], [16,10, 0,14] ]
faceIndices_345  = [
    [ 5, 6, 7, 8, 9 ],
    [0, 5, 9], [1, 6, 5], [2, 7, 6], [3, 8, 7], [4, 9, 8],
    [5, 0,10, 1], [6, 1,11, 2], [7, 2,12, 3], [8, 3,13, 4], [9, 4,14, 0],
    [0,14,10], [1,10,11], [2,11,12], [3,12,13], [4,13,14],
    [ 14,13,12,11,10 ]
]

z = np.sqrt(2) - 1
v_rmb = [
    [ z, z, 1 ], [-z, z, 1 ], [-z,-z, 1 ], [ z,-z, 1 ],
    [ 1, z, z ], [ z, 1, z ], [-z, 1, z ], [-1, z, z ], 
    [-1,-z, z ], [-z,-1, z ], [ z,-1, z ], [ 1,-z, z ],
    [ 1, z,-z ], [ z, 1,-z ], [-z, 1,-z ], [-1, z,-z ], 
    [-1,-z,-z ], [-z,-1,-z ], [ z,-1,-z ], [ 1,-z,-z ],
    [ z, z,-1 ], [-z, z,-1 ], [-z,-z,-1 ], [ z,-z,-1 ]
]
faceIndices_rmb = [
    [  0, 5, 6, 1 ], [  1, 7, 8, 2 ], [  2, 9,10, 3 ], [  3,11, 4, 0 ],
    [  4,12,13, 5 ], [  6,14,15, 7 ], [  8,16,17, 9 ], [ 10,18,19,11 ],
    [ 13,20,21,14 ], [ 15,21,22,16 ], [ 17,22,23,18 ], [ 19,23,20,12 ], 
    [  0, 1, 2, 3 ],
    [  5,13,14, 6 ], [  7,15,16, 8 ], [  9,17,18,10 ], [ 11,19,12, 4 ], 
    [ 20,23,22,21 ], 
    [  0, 4, 5 ], [  1, 6, 7 ], [  2, 8, 9 ], [  3,10,11 ],
    [  20,13,12], [ 21,15,14 ], [ 22,17,16 ], [23, 19,18 ]
]

surface_4 =   s3d.Surface3DCollection(verts,faceIndices_4)
line_4 = surface_4.edges.transform(scale=0.75)

surface_345 = s3d.Surface3DCollection(verts,faceIndices_345)
line_345 = surface_345.initedges

surface_rmb = s3d.Surface3DCollection(v_rmb,faceIndices_rmb)
line_rmb = surface_rmb.initedges

lines = [ line_4, line_345, line_rmb ]

fig = plt.figure(figsize=(8,8/3))
minmax = (-.67,.67)  
for i,line in enumerate(lines) :   
    ax =  fig.add_subplot(131+i, projection='3d', aspect='equal')
    ax.set(xlim=minmax, ylim=minmax, zlim=minmax)
    ax.set_axis_off()
    ax.set_proj_type('ortho')
    fsurface = line.shred(4).get_filled_surface(coor='c',dist=0.01, lrez=4 )
    fsurface.map_cmap_from_op( radial_Color_cyl,'rainbow_r' )
    
    ax.add_collection3d(fsurface.shade(0.4,ax=ax))

fig.tight_layout()

# =========================================================================
plt.show()