Platonic solid: icosahedron

by sonone, May 5, 2020, 8:37 PM

I'm back and have two versions of the icosahedron for you! These were fun to make!
Version 1:
[asy]
import three;
import solids;

currentprojection=orthographic(1,1.5,1);
currentlight=(0,1.5,1);
real phi=(sqrt(5)+1)/2;
real ph=phi/2;
real p=1/2;

triple[] ic;
ic[0]=(0,p,ph);
ic[1]=(0,-p,ph);
ic[2]=(0,-p,-ph);
ic[3]=(0,p,-ph);
ic[4]=(ph,0,p);
ic[5]=(ph,0,-p);
ic[6]=(-ph,0,-p);
ic[7]=(-ph,0,p);
ic[8]=(p,ph,0);
ic[9]=(-p,ph,0);
ic[10]=(-p,-ph,0);
ic[11]=(p,-ph,0);

path3[] tri;
tri[0]=ic[0]--ic[1]--ic[4]--cycle;
tri[1]=ic[1]--ic[0]--ic[7]--cycle;
tri[2]=ic[0]--ic[4]--ic[8]--cycle;
tri[3]=ic[0]--ic[8]--ic[9]--cycle;
tri[4]=ic[0]--ic[7]--ic[9]--cycle;
tri[5]=ic[8]--ic[9]--ic[3]--cycle;
tri[6]=ic[8]--ic[4]--ic[5]--cycle;
tri[7]=ic[8]--ic[3]--ic[5]--cycle;
tri[8]=ic[1]--ic[4]--ic[11]--cycle;
tri[9]=ic[1]--ic[11]--ic[10]--cycle;
tri[10]=ic[1]--ic[10]--ic[7]--cycle;
tri[11]=ic[4]--ic[5]--ic[11]--cycle;
tri[12]=ic[5]--ic[11]--ic[2]--cycle;
tri[13]=ic[11]--ic[2]--ic[10]--cycle;
tri[14]=ic[6]--ic[7]--ic[9]--cycle;
tri[15]=ic[6]--ic[7]--ic[10]--cycle;
tri[16]=ic[3]--ic[2]--ic[6]--cycle;

pen faces=royalblue;
draw(surface(tri[0]),faces);
draw(surface(tri[1]),faces);
draw(surface(tri[2]),faces);
draw(surface(tri[3]),faces);
draw(surface(tri[4]),faces);
draw(surface(tri[5]),faces);
draw(surface(tri[6]),faces);
draw(surface(tri[7]),faces);
draw(surface(tri[8]),faces);
draw(surface(tri[11]),faces);

[/asy]

Version 2:
[asy]
import three;
import solids;
currentprojection=orthographic(1,1.5,1);
currentlight=(0,1.5,1);
real phi=(sqrt(5)+1)/2;
real ph=phi/2;
real p=1/2;

triple[] ic;
ic[0]=(0,p,ph);
ic[1]=(0,-p,ph);
ic[2]=(0,-p,-ph);
ic[3]=(0,p,-ph);
ic[4]=(ph,0,p);
ic[5]=(ph,0,-p);
ic[6]=(-ph,0,-p);
ic[7]=(-ph,0,p);
ic[8]=(p,ph,0);
ic[9]=(-p,ph,0);
ic[10]=(-p,-ph,0);
ic[11]=(p,-ph,0);

path3[] tri;
tri[0]=ic[0]--ic[1]--ic[4]--cycle;
tri[1]=ic[1]--ic[0]--ic[7]--cycle;
tri[2]=ic[0]--ic[4]--ic[8]--cycle;
tri[3]=ic[0]--ic[8]--ic[9]--cycle;
tri[4]=ic[0]--ic[7]--ic[9]--cycle;
tri[5]=ic[8]--ic[9]--ic[3]--cycle;
tri[6]=ic[8]--ic[4]--ic[5]--cycle;
tri[7]=ic[8]--ic[3]--ic[5]--cycle;
tri[8]=ic[1]--ic[4]--ic[11]--cycle;
tri[9]=ic[1]--ic[11]--ic[10]--cycle;
tri[10]=ic[1]--ic[10]--ic[7]--cycle;
tri[11]=ic[4]--ic[5]--ic[11]--cycle;
tri[12]=ic[5]--ic[11]--ic[2]--cycle;
tri[13]=ic[11]--ic[2]--ic[10]--cycle;
tri[14]=ic[6]--ic[7]--ic[9]--cycle;
tri[15]=ic[6]--ic[7]--ic[10]--cycle;
tri[16]=ic[3]--ic[2]--ic[6]--cycle;


pen faces=royalblue;
draw(surface(tri[0]),faces,nolight);
draw(surface(tri[1]),faces,nolight);
draw(surface(tri[2]),faces,nolight);
draw(surface(tri[3]),faces,nolight);
draw(surface(tri[4]),faces,nolight);
draw(surface(tri[5]),faces,nolight);
draw(surface(tri[6]),faces,nolight);
draw(surface(tri[7]),faces,nolight);
draw(surface(tri[8]),faces,nolight);
draw(tri[9],dotted);
draw(tri[10],dotted);
draw(surface(tri[11]),faces,nolight);
draw(tri[12],dotted);
draw(tri[13],dotted);
draw(tri[14],dotted);
draw(tri[15],dotted);
draw(tri[16],dotted);
for(int i=0; i<=8; ++i){
draw(tri[i]);
}
draw(tri[11]);
[/asy]

Comment

1 Comment

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Very nice! You did a good job with the shading on the first one!

by G.G.Otto, May 6, 2020, 7:07 PM

Old material is mostly Asymptote, new material is calculator programming

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sonone
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  • I still exist as well.

    by G.G.Otto, Aug 11, 2023, 2:44 AM

  • hello I'm still here lol

    by player01, Aug 6, 2022, 6:24 PM

  • [REVIVAL] I will start posting more calculator relating posts very soon. Even though school has been busy, I have been programming my calculators a decent amount, so I have a lot to share...

    by sonone, Feb 18, 2022, 10:29 PM

  • wow its been like 2.5 years since geo class

    by pieMax2713, Feb 4, 2022, 8:38 PM

  • @violin21, I've been very busy with school lately and haven't been able to add another lesson. I will when i get a free moment

    by sonone, Aug 19, 2021, 12:45 AM

  • ORZ CODER

    by samrocksnature, Aug 9, 2021, 9:57 PM

  • Could you make more Asymptote lessons on your "How to do Asymptote" blog?

    by violin21, Aug 9, 2021, 7:26 PM

  • You can take it, just C&P the CSS into your CSS area

    by sonone, Apr 17, 2021, 10:08 PM

  • how can we take the CSS if we have permission to not take it?

    by GoogleNebula, Apr 17, 2021, 5:22 PM

  • That is awesome!

    by sonone, Apr 15, 2021, 10:09 PM

  • I modified your dodecahedron and got:
    [asy]
    import three;
    import solids;
    size(300);
    currentprojection=orthographic(0,1.3,1.2);
    light(0,5,10);

    real phi=(sqrt(6)+1)/3;
    real g=(phi-1)/2;
    real s=1/2;
    real a=sqrt(1-phi*phi/4-g*g)+phi/2;

    triple[] d;
    d[0]=(phi

    by Andrew2019, Mar 26, 2021, 12:15 AM

  • Not too many, just changing the color here and there. I really like your CSS!

    by sonone, Feb 2, 2021, 10:35 AM

  • Nice!

    I see you're making changes to the CSS. :)

    by G.G.Otto, Feb 1, 2021, 9:26 PM

  • I'm learning Java now!

    by sonone, Feb 1, 2021, 5:56 PM

  • And I took part of it from CaptainFlint and then added a ton of modifications. ;)

    by G.G.Otto, Dec 1, 2020, 8:56 AM

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