Python, 73 bytes

x={3*(55,),(89,34,0)} for s in(-1,1)*3:x|={(s*y,*z)for*z,y in x} print(x) 

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Retired Python, 103 bytes

*x,x[7],x[2]=6*[-55,55] *y,y[11],_,_,y[2]=3*[-34,0,-89,34,0,89] for a in x,y:*map(print,a,a[1:],a[2:]), 

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Integer coordinates from @alephalpha / @xnor via @Arnauld.

Python, 73 bytes

x={3*(55,),(89,34,0)} for s in(-1,1)*3:x|={(s*y,*z)for*z,y in x} print(x) 

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Same approach as @xnor (I think), i.e. flip signs and rotate coordinates random-ish-ly. Only, I'm being more simple-minded about it ;-)

Retired Python, 103 bytes

*x,x[7],x[2]=6*[-55,55] *y,y[11],_,_,y[2]=3*[-34,0,-89,34,0,89] for a in x,y:*map(print,a,a[1:],a[2:]), 

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Integer coordinates from @alephalpha / @xnor via @Arnauld.

Python, 103 bytes

*x,x[7],x[2]=6*[-55,55] *y,y[11],_,_,y[2]=3*[-34,0,-89,34,0,89] for a in x,y:*map(print,a,a[1:],a[2:]), 

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Integer coordinates from @alephalpha / @xnor via @Arnauld.

Python, 73 bytes

x={3*(55,),(89,34,0)} for s in(-1,1)*3:x|={(s*y,*z)for*z,y in x} print(x) 

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Retired Python, 103 bytes

*x,x[7],x[2]=6*[-55,55] *y,y[11],_,_,y[2]=3*[-34,0,-89,34,0,89] for a in x,y:*map(print,a,a[1:],a[2:]), 

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Integer coordinates from @alephalpha / @xnor via @Arnauld.