I haven't found any examples of antique blocks or quilts by the name of Missouri Star.
If you have Electric Quilt's Blockbase program, the Missouri Star block is #2154.
There is a paper pieced pattern at Quilter's Cache for a 12" block.
There is a tutorial for making this Missouri Star quilt block at Sewing by Moonlight.
I put my 6" block together like this-
The center starts out as a 3 1/2" square. Two inch squares are added at each corner and sewn diagonally and flipped back to form the corner triangles as shown above. Four two inch squares are needed for the corners.
To make the quarter square triangles, I first made four half square triangles from two 2 3/4" squares of white fabric and two squares of red fabric placed right sides together, marked on the diagonal and sewn 1/4" on each side of the diagonal line as shown above. Cut on the diagonal line after sewing and you have two half square triangles.
The diagram above shows one half square triangle and the steps needed to make the quarter square triangles. The first photo is one half of the square cut on the diagonal, the second photo shows the square pressed open and the last photo shows the half square triangle cut diagonally to make two quarter square triangles.
To make the sides, cut a 4 3/16" square of background fabric into four triangles by cutting on both diagonal lines. These are the centers of each side piece. Sew one quarter square triangle to each short side of your side triangles. You also need to cut four 2" squares from your background fabric.
Arrange your pieces as shown above, sew together in rows and sew the rows together. This is a very easy block!