CoCalc Public Filesunits2021 / groups / sessions / group-actions.ipynbOpen with one click!
Author: Killian O'Brien
Views : 120
Description: Rotate the platonic solids, drawn slightly transparent with prominent edges and vertices to aid visualization.
Compute Environment: Ubuntu 18.04 (Stable)
In [7]:
G = Graphics() # an empty graphics object # create an orange dodecahedron D and add it to G # try the other platonic solid polyheda: # tetrahedron, cube, octagon, icosahedron D = dodecahedron(color='orange', opacity=0.85) G += D # add lines to G for each edge of D for e in D.edges(): G += line3d(e,color='black',thickness=5) # add dots to G for each vertex of D for v in D.vertices(): G += point3d(v,size=15,color='black') # add the face labels 1,..,12 flabel = 0 n = len(D.face_list()[0]) # number of vertices per face for f in D.faces(): flabel += 1 c = 1/n*sum(vector(v) for v in f) # the face center c = 1.1*c # out a bit # comment out next line to suppress the label printing G += text3d(str(flabel), c, color=(0,0,0)) # add the vertex labels a,b,c,... vlabels = 'abcdefghijklmnopqrstuvwxyz' i = 0 for v in D.vertices(): v = 1.08 * vector(v) # out a bit # comment out next line to suppress the label printing G += text3d(vlabels[i], v, color=(0,0,0)) i += 1 # look at G show(G,frame=False)
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In [5]:
1/24*(3^8+6*3^2+17*3^4)
333
In [8]:
RR(6561/333)
19.7027027027027
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