with(plots): p1:=sphere([0,0,0],1): p2:=polygon([[-1,1,1],[1,-1,1],[1,1,-1]]); p3:=polygon([[-1,-1,-1],[1,-1,1],[1,1,-1]]); p4:=polygon([[-1,1,1],[-1,-1,-1],[1,1,-1]]); p5:=polygon([[-1,1,1],[1,-1,1],[-1,-1,-1]]); display(p1,p2,p3,p4,p5);

p:=expand((1-u)*[cos(t),sin(t),1]+u*[1,sin(t),1]);

with(linalg):

q:=expand(sqrt(2)*p/norm(p,2));

r1:=plot3d(q,t=0..Pi/2,u=0..1):

with(plots):with(plottools):

r2:=rotate(r1,2*Pi/3,[[0,0,0],[1,1,1]]):

r3:=rotate(r1,4*Pi/3,[[0,0,0],[1,1,1]]):

u1:=display(r1,r2,r3):

u2:=rotate(u1,0,0,Pi/2):

u3:=rotate(u1,0,0,Pi):

u4:=rotate(u1,0,0,3*Pi/2):

v1:=display(u1,u2,u3,u4,scaling=constrained):

v2:=reflect(v1,[0,0,0]):

with(plots):with(geom3d):

p1:=display(draw(cube(c,point(o,0,0,0),sqrt(3)))):

p2:=display(draw(sphere(s,[point(o,0,0,0),sqrt(2)]))):

p1:=plot3d(1,theta=0..2*Pi,phi=0..Pi/4,coords=spherical,scaling=constrained):

with(plottools):

q1:=translate(p1,0,0,-sqrt(2)):

q2:=rotate(q1,0,Pi/2,0):

q3:=rotate(q1,0,Pi,0):

q4:=rotate(q1,0,3*Pi/2,0):

q5:=rotate(q1,Pi/2,0,0):

q6:=rotate(q1,3*Pi/2,0,0):

with(plots):