File:Csaszar polyhedron.stl

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English: Császár polyhedron (one of only two diagonal-less polyhedra) by CMG Lee.
Source Own work
Author Cmglee

Python source

#!/usr/bin/env python

# header    = 'Cs\xe1sz\xe1r polyhedron (one of only two diagonal-less polyhedra) by CMG Lee.' ## non-ASCII characters hex-encoded
header    = 'Csaszar polyhedron (one of only two diagonal-less polyhedra) by CMG Lee.'
vertexsss = [ ## [i_vertex][property][x,y,z etc]
             {'xyz':(-6, 6,-6), 'colour':'#c00', 'label':'G'},
             {'xyz':(-6,-6,-5), 'colour':'#090', 'label':'C'},
             {'xyz':(-2,-3, 0), 'colour':'#069', 'label':'D'},
             {'xyz':( 2, 3, 0), 'colour':'#c60', 'label':'E'},
             {'xyz':( 6, 6,-5), 'colour':'#c0f', 'label':'F'},
             {'xyz':( 6,-6,-6), 'colour':'#00f', 'label':'B'},
             {'xyz':( 0, 0, 6), 'colour':'#000', 'label':'A'}]
facesss = [ ## [i_face][property][i_vertex etc]
           {'vertexs':[0,2,3], 'flip':True , 'colour':'#f00'}, ## face down 1
           {'vertexs':[2,3,5], 'flip':False, 'colour':'#00f'}, ## face down 2
           {'vertexs':[1,2,4], 'flip':False, 'colour':'#069'}, ## bottom inner 1
           {'vertexs':[1,3,4], 'flip':True , 'colour':'#960'}, ## bottom inner 2
           {'vertexs':[1,2,6], 'flip':True , 'colour':'#0f0'}, ## top inner 1
           {'vertexs':[3,4,6], 'flip':False, 'colour':'#f0f'}, ## top inner 2
           {'vertexs':[2,4,5], 'flip':True , 'colour':'#09f'}, ## bottom outer 2
           {'vertexs':[0,1,3], 'flip':False, 'colour':'#f90'}, ## bottom outer 2
           {'vertexs':[0,2,6], 'flip':False, 'colour':'#ff0'}, ## top outer 1
           {'vertexs':[3,5,6], 'flip':True , 'colour':'#ccc'}, ## top outer 2
           {'vertexs':[0,4,6], 'flip':True , 'colour':'#f66'}, ## outside 1
           {'vertexs':[1,5,6], 'flip':False, 'colour':'#66f'}, ## outside 2
           {'vertexs':[0,4,5], 'flip':False, 'colour':'#606'}, ## base 1
           {'vertexs':[0,1,5], 'flip':True , 'colour':'#060'}] ## base 2

import re, struct, math
def fmt(string): ## string.format(**vars()) using tags {expression!format} by CMG Lee
 def f(tag): i_sep = tag.rfind('!'); return (re.sub('\.0+$', '', str(eval(tag[1:-1])))
  if (i_sep < 0) else ('{:%s}' % tag[i_sep + 1:-1]).format(eval(tag[1:i_sep])))
 return (re.sub(r'(?<!{){[^{}]+}', lambda m:f(, string)
         .replace('{{', '{').replace('}}', '}'))
def append(obj, string): return obj.append(fmt(string))
def tabbify(cellss, separator='|'):
 cellpadss = [list(rows) + [''] * (len(max(cellss, key=len)) - len(rows)) for rows in cellss]
 fmts = ['%%%ds' % (max([len(str(cell)) for cell in cols])) for cols in zip(*cellpadss)]
 return '\n'.join([separator.join(fmts) % tuple(rows) for rows in cellpadss])
def hex_rgb(colour): ## convert [#]RGB to #RRGGBB and [#]RRGGBB to #RRGGBB
 return '#%s' % (colour if len(colour) > 4 else ''.join([c * 2 for c in colour])).lstrip('#')
def viscam_colour(colour):
 colour_hex      = hex_rgb(colour)
 colour_top5bits = [int(colour_hex[i:i+2], 16) >> 3 for i in range(1,7,2)]
 return (1 << 15) + (colour_top5bits[0] << 10) + (colour_top5bits[1] << 5) + colour_top5bits[2]
def roundm(x, multiple=1):
 if   (isinstance(x, tuple)): return tuple(roundm(list(x), multiple))
 elif (isinstance(x, list )): return [roundm(x_i, multiple) for x_i in x]
 else: return int(math.floor(float(x) / multiple + 0.5)) * multiple
def flatten(lss): return [l for ls in lss for l in ls]
def rotate(facetss, degs): ## around x then y then z axes
 (deg_x,deg_y,deg_z) = degs
 (sin_x,cos_x) = (math.sin(math.radians(deg_x)), math.cos(math.radians(deg_x)))
 (sin_y,cos_y) = (math.sin(math.radians(deg_y)), math.cos(math.radians(deg_y)))
 (sin_z,cos_z) = (math.sin(math.radians(deg_z)), math.cos(math.radians(deg_z)))
 facet_rotatess = []
 for facets in facetss:
  facet_rotates = []
  for i_point in range(4):
   (x, y, z) = [facets[3 * i_point + i_xyz] for i_xyz in range(3)]
   if (x is None or y is None or z is None):
    facet_rotates += [x, y, z]
    (y, z) = (y * cos_x - z * sin_x,  y * sin_x + z * cos_x) ## rotate about x
    (x, z) = (x * cos_y + z * sin_y, -x * sin_y + z * cos_y) ## rotate about y
    (x, y) = (x * cos_z - y * sin_z,  x * sin_z + y * cos_z) ## rotate about z
    facet_rotates += [round(value, 9) for value in [x, y, z]]
 return facet_rotatess
def translate(facetss, ds): ## ds = (dx,dy,dz)
 return [facets[:3] + [facets[3 * i_point + i_xyz] + ds[i_xyz]
                       for i_point in range(1,4) for i_xyz in range(3)]
         for facets in facetss]

## Add facets
facetss = []
for facess in facesss:
 vertexs        = facess['vertexs']
 vertex_facetss = [vertexsss[i_vertex]['xyz']
                   for i_vertex in (vertexs[::-1] if (facess['flip']) else vertexs)]
 facetss.append(flatten([(None,0,0)] + vertex_facetss + [[facess['colour']]]))
# facetss = [facets[:3] + facets[6:9] + facets[3:6] + facets[9:] for facets in facetss]

## Calculate normals
for facets in facetss:
 if (facets[0] is None or facets[1] is None or facets[2] is None):
  us      = [facets[i_xyz + 9] - facets[i_xyz + 6] for i_xyz in range(3)]
  vs      = [facets[i_xyz + 6] - facets[i_xyz + 3] for i_xyz in range(3)]
  normals = [us[1]*vs[2] - us[2]*vs[1], us[2]*vs[0] - us[0]*vs[2], us[0]*vs[1] - us[1]*vs[0]]
  normal_length = sum([component * component for component in normals]) ** 0.5
  facets[:3] = [-round(component / normal_length, 10) for component in normals]

print(tabbify([['N%s'  % (xyz   )                   for xyz in list('xyz')] +
               ['%s%d' % (xyz, n) for n in range(3) for xyz in list('XYZ')] + ['RGB']] + facetss))
## Compile STL
outss = ([[('STL\n\n%-73s\n\n' % (header[:73])).encode('utf-8'), struct.pack('<L',len(facetss))]] +
         [[struct.pack('<f',float(value)) for value in facets[:12]] +
          [struct.pack('<H',0 if (len(facets) <= 12) else
                            viscam_colour(facets[12]))] for facets in facetss])
out   = b''.join([bytes(out) for outs in outss for out in outs])
# out += ('\n\n## Python script to generate STL\n\n%s\n' % (open(__file__).read())).encode('utf-8')
print("# bytes:%d\t# facets:%d\ttitle:\"%-73s\"" % (len(out), len(facetss), header[:73]))
with open(__file__[:__file__.rfind('.')] + '.stl', 'wb') as f_out: f_out.write(out)


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The uploader of this file has agreed to the Wikimedia Foundation 3D patent license: This file and any 3D objects depicted in the file are both my own work. I hereby grant to each user, maker, or distributor of the object depicted in the file a worldwide, royalty-free, fully-paid-up, nonexclusive, irrevocable and perpetual license at no additional cost under any patent or patent application I own now or in the future, to make, have made, use, offer to sell, sell, import, and distribute this file and any 3D objects depicted in the file that would otherwise infringe any claims of any patents I hold now or in the future.

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28 March 2018


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current08:45, 29 March 2018Thumbnail for version as of 08:45, 29 March 2018 (784 bytes)wikimediacommons>CmgleeRotate, and reduce height to better show hole.

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