Add a Circle and set its vertices number to 10.
Scale and rotate it to fit the picture using snapping tool (click on a magnet icon and set its type to Increment). Hold down Shift while rotating to do it precisely. [In this case i rotated a circle 18 degress]. Being in Edit Mode select the whole circle (A), then pres W-->Subdivide.
Delete one half of a mesh and give it a Mirror Modifier. Extrude the vertices to fit the reference image.
Apply a Mirror Modifier and then add a Subsurf Modifier. Select the outer edges and press Alt+Shift+S (with a cursor snapped to an origin point) to make them spherical.
Now set the pivot point to Individual Origins. Select the faces as pictured below, then press I and I again to inset the individual faces. Repeat the process with other faces.
Select the edges as pictured below, press G then Z. Select all edges and sharpen them using Shift+E shortcut.
Give it a proper shape using Lattice Modifier and proportional editing. Give it some thickness using Solidify Modifier.