What equation is Statsmodels OLS using to create example fit line - python-3.x

Question

I'm a novice to statics analysis and was looking into using statsmodels. As part of my research I ran into the following set of examples.
The section "OLS Non-linear curve but liner in parameters" is confusing the heck out of me. Example Follows:
np.random.seed(9876789)
nsample = 50
sig = 0.5
x = np.linspace(0, 20, nsample)
X = np.column_stack((x, np.sin(x), (x-5)**2, np.ones(nsample)))
beta = [0.5, 0.5, -0.02, 5.]
y_true = np.dot(X, beta)
y = y_true + sig * np.random.normal(size = nsample)
res = sm.OLS(y, X).fit()
print(res.summary())
This shows the following summary results:
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.933
Model: OLS Adj. R-squared: 0.928
Method: Least Squares F-statistic: 211.8
Date: Tue, 28 Feb 2017 Prob (F-statistic): 6.30e-27
Time: 21:33:30 Log-Likelihood: -34.438
No. Observations: 50 AIC: 76.88
Df Residuals: 46 BIC: 84.52
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
x1 0.4687 0.026 17.751 0.000 0.416 0.522
x2 0.4836 0.104 4.659 0.000 0.275 0.693
x3 -0.0174 0.002 -7.507 0.000 -0.022 -0.013
const 5.2058 0.171 30.405 0.000 4.861 5.550
==============================================================================
Omnibus: 0.655 Durbin-Watson: 2.896
Prob(Omnibus): 0.721 Jarque-Bera (JB): 0.360
Skew: 0.207 Prob(JB): 0.835
Kurtosis: 3.026 Cond. No. 221.
==============================================================================
When you plot all of this you get:
Plot of Data, Fit and True Line
What's confusing me is I can't figure out how the fit comes out of the coefficients shown in the summary table. My understanding is that these coefficients for the linear fit should correspond to and equation in the format X1 * x^3 + X2 * X^2 + X3 * X + Const, but that does not result in the curve seen. My next thought was that it might have been extrapolating the equation based on the values in the X matrix, therefore something like X1 * x + X2 * sin(x) + X3 * (x-5)^2 + Const. That also does not work.
What does seem to work is a polynomial fit with a degree of around 10. I found that using np.polyfit(x, y, 10). (The Coefficients of which are not similar to the OLS ones, plus there's 6 more)
So my question is what equation is OLS using to produce the predicted values? How doe the coefficients relate to it? When no equation is specified (assuming it's using something different than normal polynomial equations) how does it determine what to use or whats the best fit?
One Note, I've figured out that I can force it to do what I was expecting by changing the x values used to a different matrix via np.vander()
X = np.vander(X, 4)
This produces results in line with what I was expecting and np.polyfit.