R help - Mar 2014 - fitting

given the data below 



x1<-c(-1,0,1,-1,0,1,-1,0,1,-1,0,1,-1,0,1,-1,0,1,-1,0,1,-1,0,1,-1,0,1)
y<-c(-1,-1,-1,0,0,0,1,1,1,-1,-1,-1,0,0,0,1,1,1,-1,-1,-1,0,0,0,1,1,1)
z<-c(-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1)

using maple i can fit as below and get (1)

#PolynomialFit(3, x1, y1, z) ;

Fit(a+b*(x^2+y^2+z^2), Matrix([x1,y1,z1]),m1,[x,y,z]);

(1)



my question, is there a way we can do the same in R (i.e to obtain (1) using R)

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