:name dodecahedron :number 3 :symbol {5,3} @D sub 5 @ :dual icosahedron :sfaces 12 12{5} :svertices 20 20(@5 sup 3@) :net 12 5 5 10 16 23 24 17 5 37 32 24 23 31 5 25 18 17 24 30 5 4 3 10 17 11 5 1 9 16 10 2 5 22 29 23 16 15 5 15 8 14 21 22 5 0 5 13 14 6 5 12 19 20 13 7 5 33 34 27 20 26 5 36 28 21 27 35 5 27 21 14 13 20 :solid 12 5 5 40 38 39 42 43 5 49 48 42 39 44 5 54 50 43 42 48 5 51 46 40 43 50 5 47 41 38 40 46 5 45 44 39 38 41 5 41 47 53 52 45 5 46 51 56 53 47 5 50 54 57 56 51 5 48 49 55 57 54 5 44 45 52 55 49 5 55 52 53 56 57 :hinges 11 0 0 4 2 2.0344439357957027 0 1 5 2 2.0344439357957027 0 2 1 2 2.0344439357957027 0 3 2 2 2.0344439357957027 0 4 3 2 2.0344439357957027 5 4 6 4 2.0344439357957027 11 0 10 2 2.0344439357957027 11 1 6 2 2.0344439357957027 11 2 7 2 2.0344439357957027 11 3 8 2 2.0344439357957027 11 4 9 2 2.0344439357957027 :dih 1 30 5 5 2.0344439357957027 :vertices 58 38 -1.80170732464719[(-3/16+(-3/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-3/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -3.92705098312484[(-9/4+(-3/4)*sqrt(5))] 0[0] -1.80170732464719[(-5/16+(-3/80)*sqrt(5))*sqrt(10+2*sqrt(5))-1/8*sqrt(10-2*sqrt(5))] -1.30901699437495[(-3/4+(-1/4)*sqrt(5))] 0[0] -1.80170732464719[(-3/16+(-3/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-3/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -.309016994374947[(1/4+(-1/4)*sqrt(5))] 0[0] -1.80170732464719[(-1/16+(-13/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(1/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] .309016994374947[(-1/4+(1/4)*sqrt(5))] 0[0] -1.80170732464719[(-3/16+(-13/80)*sqrt(5))*sqrt(10+2*sqrt(5))+1/8*sqrt(10-2*sqrt(5))] 1.30901699437495[(3/4+(1/4)*sqrt(5))] 0[0] -1.21392207235472[(-5/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-3/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -4.73606797749979[(-5/2-sqrt(5))] 0[0] -1.21392207235472[(-5/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-3/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -3.11803398874989[(-2+(-1/2)*sqrt(5))] 0[0] -.85065080835204001[(1/4+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))+(-7/16+(-3/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -5.23606797749979[(-3-sqrt(5))] 0[0] -.85065080835204001[(1/4+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))+(-7/16+(-3/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -2.61803398874989[(-3/2+(-1/2)*sqrt(5))] 0[0] -.85065080835204001[(-3/16+(-3/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-1/16+(1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -1.61803398874989[(-1/2+(-1/2)*sqrt(5))] 0[0] -.85065080835204001[(-1/10)*sqrt(5)*sqrt(10+2*sqrt(5))] 0[0] 0[0] -.85065080835204001[(-1/16+(-13/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(3/16+(1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] 1.61803398874989[(1/2+(1/2)*sqrt(5))] 0[0] -.262865556059567[(1/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-1/4+(-1/8)*sqrt(5))*sqrt(10-2*sqrt(5))] -6.04508497187474[(-13/4+(-5/4)*sqrt(5))] 0[0] -.262865556059567[(3/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-5/16+(-3/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -4.42705098312484[(-11/4+(-3/4)*sqrt(5))] 0[0] -.262865556059567[(3/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-5/16+(-3/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -3.42705098312484[(-7/4+(-3/4)*sqrt(5))] 0[0] -.262865556059567[(1/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-1/4+(-1/8)*sqrt(5))*sqrt(10-2*sqrt(5))] -1.80901699437495[(-5/4+(-1/4)*sqrt(5))] 0[0] -.262865556059567[(-1/8+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))] -.80901699437494701[(-1/4+(-1/4)*sqrt(5))] 0[0] -.262865556059567[(-1/8+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))] .80901699437494701[(1/4+(1/4)*sqrt(5))] 0[0] -.262865556059567[(-3/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))-1/8*sqrt(10-2*sqrt(5))] 1.80901699437495[(5/4+(1/4)*sqrt(5))] 0[0] .688190960235587[(1/4+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))+(-1/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -5.73606797749979[(-7/2-sqrt(5))] 0[0] .688190960235587[(3/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-3/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -4.73606797749979[(-5/2-sqrt(5))] 0[0] .688190960235587[(3/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(-3/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -3.11803398874989[(-2+(-1/2)*sqrt(5))] 0[0] .688190960235587[(1/4+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))+(-1/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -2.11803398874989[(-1+(-1/2)*sqrt(5))] 0[0] .688190960235587[(1/8+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))] -.5[-1/2] 0[0] .688190960235587[(1/8+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))] .5[1/2] 0[0] .688190960235587[(1/40)*sqrt(5)*sqrt(10+2*sqrt(5))+(1/16+(1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] 2.11803398874989[(1+(1/2)*sqrt(5))] 0[0] 1.27597621252806[(1/8+(11/40)*sqrt(5))*sqrt(10+2*sqrt(5))+(-3/8+(-1/8)*sqrt(5))*sqrt(10-2*sqrt(5))] -5.54508497187474[(-11/4+(-5/4)*sqrt(5))] 0[0] 1.27597621252806[(3/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(1/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -3.92705098312484[(-9/4+(-3/4)*sqrt(5))] 0[0] 1.27597621252806[(1/4+(3/20)*sqrt(5))*sqrt(10+2*sqrt(5))+(-1/8+(-1/8)*sqrt(5))*sqrt(10-2*sqrt(5))] -2.30901699437495[(-7/4+(-1/4)*sqrt(5))] 0[0] 1.27597621252806[(1/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+1/8*sqrt(10-2*sqrt(5))] -1.30901699437495[(-3/4+(-1/4)*sqrt(5))] 0[0] 1.27597621252806[(-3/16+(7/80)*sqrt(5))*sqrt(10+2*sqrt(5))+(1/4+(1/8)*sqrt(5))*sqrt(10-2*sqrt(5))] 1.30901699437495[(3/4+(1/4)*sqrt(5))] 0[0] 1.63924747653074[(3/8+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))] -.80901699437494701[(-1/4+(-1/4)*sqrt(5))] 0[0] 1.63924747653074[(3/8+(1/40)*sqrt(5))*sqrt(10+2*sqrt(5))] .80901699437494701[(1/4+(1/4)*sqrt(5))] 0[0] 2.22703272882321[(1/4+(11/40)*sqrt(5))*sqrt(10+2*sqrt(5))+(-5/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] -5.23606797749979[(-3-sqrt(5))] 0[0] 2.22703272882321[(1/8+(11/40)*sqrt(5))*sqrt(10+2*sqrt(5))-1/4*sqrt(10-2*sqrt(5))] -4.23606797749979[(-2-sqrt(5))] 0[0] 2.22703272882321[(1/4+(3/20)*sqrt(5))*sqrt(10+2*sqrt(5))] -3.61803398874989[(-5/2+(-1/2)*sqrt(5))] 0[0] 2.22703272882321[(3/8+(3/20)*sqrt(5))*sqrt(10+2*sqrt(5))+(-1/16+(-1/16)*sqrt(5))*sqrt(10-2*sqrt(5))] 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