${\displaystyle [-10,10]^{3}}$

${\displaystyle Tog=64(x-w)(x^{4}-4x^{3}w-10x^{2}y^{2}-4x^{2}w^{2}+16xw^{3}-20xy^{2}w+5y^{4}+16w^{4}-20y^{2}w^{2})\,\!\!}$ ${\displaystyle -5{\sqrt {5-{\sqrt {5}}}}(2z-{\sqrt {5-{\sqrt {5}}}}w)(4(x^{2}+y^{2}-z^{2})+(1+3{\sqrt {5}})w^{2})^{2}}$

Created using SageMath 8.7.

sage: def Tog(x,y,z,w):
....:     return 64*(x-w)*(x^4 -4*x^3*w -10*x^2*y^2 -4*x^2*w^2 +16*x*w^3 -20*x*y^2*w
....: +5*y^4 +16*w^4 -20*y^2*w^2) -5*sqrt(5-sqrt(5))*(2*z -sqrt(5-sqrt(5))*w)*
....: (4*(x^2+y^2-z^2) +(1+3*sqrt(5))*w^2)^2
sage: var('x,y,z')
sage: g=implicit_plot3d(Tog(x,y,z,1),(x,-10,10),(y,-10,10),(z,-10,10),smooth=True,plot_points=200)
sage: g.save("tog.stl")