restart;

x:=cos(t);

y:=sin(t);

scaling=constrained);

restart;

x:=cos(t);

y:=sin(t);

with(plottools):

p1:=plot3d([x,y,z],t=0..2*Pi,z=-1..x,scaling=constrained):

p2:=reflect(p1,[[0,0,0],[1,0,1],[1,2,1]]):

with(plots):

restart;

with(plots):

with(plottools):

x:=cos(t);

y:=sin(t);

p1:=plot3d([x,y,z],t=-Pi/3..Pi/3,z=-1.2..-1/sqrt(2)*x,scaling=constrained,grid=[31,5]):

p2:=rotate(p1,0,0,2*Pi/3):

p3:=rotate(p1,0,0,4*Pi/3):

q1:=display(p1,p2,p3):

q2:=reflect(q1,[[0,0,0],[1,0,-1/sqrt(2)],[1,1,-1/sqrt(2)]]:

q3:=rotate(q2,0,0,2*Pi/3):

q4:=rotate(q2,0,0,4*Pi/3):

restart;

with(plots):

with(plottools):

x:=cos(t);

y:=sin(t);

p1:=plot3d([x,y,z],t=-Pi/3..Pi/3,z=-1.6..-sqrt(2)*x,scaling=constrained,grid=[31,5]):

p2:=rotate(p1,0,0,2*Pi/3):

p3:=rotate(p1,0,0,4*Pi/3):

q1:=display(p1,p2,p3):

q2:=reflect(q1,[[0,0,0],[1,0,-sqrt(2)],[1,1,-sqrt(2)]]):

q3:=rotate(q2,0,0,2*Pi/3):

q4:=rotate(q2,0,0,4*Pi/3):

r1:=display(q1,q2,q3,q4):

r2:=reflect(r1,[0,0,0]):

display(r1,r2);

restart;

with(plots):

tau:=(sqrt(5)+1)/2;

p1:=plot3d([u,v,0],u=-tau..tau,v=-1..1,scaling=constrained,grid=[5,5]):

p2:=plot3d([0,u,v],u=-tau..tau,v=-1..1,scaling=constrained,grid=[5,5]):

> p3:=plot3d([v,0,u],u=-tau..tau,v=-1..1,scaling=constrained,grid=[5,5]):

restart;

with(plots):

with(plottools):

tau:=(sqrt(5)+1)/2;

x:=cos(t);

y:=sin(t);

p1:=plot3d([x,y,z],t=-Pi/5..Pi/5,z=-1.8..-tau*x,scaling=constrained,grid=[21,5]):

p2:=rotate(p1,0,0,2*Pi/5):

p3:=rotate(p1,0,0,4*Pi/5):

p4:=rotate(p1,0,0,6*Pi/5):

p5:=rotate(p1,0,0,8*Pi/5):

q1:=display(p1,p2,p3,p4,p5):

q2:=reflect(q1,[[0,0,0],[1,0,-tau],[1,1,-tau]]):

q3:=rotate(q2,0,0,2*Pi/5):

q4:=rotate(q2,0,0,4*Pi/5):

q5:=rotate(q2,0,0,6*Pi/5):

q6:=rotate(q2,0,0,8*Pi/5):

r1:=display(q1,q2,q3,q4,q5,q6):

r2:=reflect(r1,[0,0,0]):

display(r1,r2);

restart;

with(geom3d):

with(plots):

tau:=(sqrt(5)+1)/2;

p1:=plot3d([v,u,0],u=-tau..tau,v=-1/tau..1/tau,scaling=constrained,grid=[5,5]):

p2:=plot3d([0,v,u],u=-tau..tau,v=-1/tau..1/tau,scaling=constrained,grid=[5,5]):

p3:=plot3d([u,0,v],u=-tau..tau,v=-1/tau..1/tau,scaling=constrained,grid=[5,5]):

cube(c,point(o,[0,0,0]),sqrt(3));

p4:=draw(c):

dodecahedron(dod,point(o,[0,0,0]),sqrt(3));

p5:=display(draw(dod),style=wireframe,thickness=5,color=black):

restart;

t:=2*Pi/5;

with(plots): with(plottools):

p1:=polygon([[2*cos(t),2*sin(t),1],[2*cos(2*t),2*sin(2*t),1],[2*cos(3*t),2*sin(3*t),1],[2*cos(4*t),2*sin(4*t),1],[2*cos(5*t),2*sin(5*t),1]]):

p2:=reflect(p1,[0,0,0]):

q1:=display(p1,p2,scaling=constrained):

q2:=rotate(q1,2*Pi/5,[[0,0,0],[2*cos(t),2*sin(t),1]]):

q3:=rotate(q1,2*Pi/5,[[0,0,0],[2*cos(2*t),2*sin(2*t),1]]):

q4:=rotate(q1,2*Pi/5,[[0,0,0],[2*cos(3*t),2*sin(3*t),1]]):

q5:=rotate(q1,2*Pi/5,[[0,0,0],[2*cos(4*t),2*sin(4*t),1]]):

q6:=rotate(q1,2*Pi/5,[[0,0,0],[2*cos(5*t),2*sin(5*t),1]]):

display(q1,q2,q3,q4,q5,q6);