  We add two new 1-parameter families to the short list of known embedded
triply periodic minimal surfaces of genus 4 in $\mathbb{R}^3$. Both surfaces
can be tiled by minimal pentagons with two straight segments and three planar
symmetry curves as boundary. In one case (which has the appearance of the CLP
surface of Schwarz with an added handle) the two straight segments are
parallel, while they are orthogonal in the second case. The second family has
as one limit the Costa surface, showing that this limit can occur for triply
periodic minimal surfaces. For the existence proof we solve the 1-dimensional
period problem through a combination of an asymptotic analysis of the period
integrals and geometric methods.
  v2: corrected embeddedness proof. Minor further improvements.
