Thickening the edges of the tetrahedron yields a genus 3 surface with a tetrahedral group action. Kerckhoff's theorem ensures that there exists a complex structure on the surface such that the action is holomorphic. Regard this Riemann surface as an algebraic curve, M. Oka then asked "What is its defining equation?" In this talk, we explicitly give the defining equation. Unexpectedly it is not unique but contains a parameter, giving a 1-parameter family of algebraic curves together with a sporadic hyperelliptic curve. We subsequently describe the image of this family under the moduli map into the moduli space of genus 3 curves. The image is a curve in the moduli space passing through the Fermat point and the Klein point. We next describe the universal family around the Fermat point by means of the theory of quotient families developed by S. Takamura.