20 Mentai: 8 Hexagons & 12 Pentagons (S12)

This marking is quite popular, being used often in the Japanese books. It creates 20 faces in resulting in 2 regular hexagons, one each at the north and south poles. In addition there are 12 irregular pentagons and 6 irregular hexagons. 6 of the pentagons surround  each of the hexagons located at the poles; the hexagons circumscribe the equator.

Begin by marking a Simple 12 using waste thread (it will be removed and discarded as the marking is completed, so usually something like a basting thread is applicable). Don't mark the equator with thread, but do place pins at the equator points on each of the Simple 12 lines.

It will help for to have an assortment of colored pins, using a different color for each step.

 Determine the distance from the equator to the NP. Divide this distance into thirds. Pin 1/3 of the equator-pole distance on every other marking line (yellow pins A & B in photo to the left). Repeat on southern hemisphere.  Orange pins are the equator points.
 On the alternate marking lines that do not have marking pins, place a pin 1/4 the distance of pole to equator, in both hemispheres.  These are shown as red pins C in the photo to the left. All work from this point forward using the desired marking thread for the design. Stitch the outline of the north polar hexagon, using the uppermost set of yellow pins. When complete, take the thread down to one of the B pins.

 Stitch the zig zag from Pins B to C etc around to where you began. Repeat the zig zag line around the B and C pins on the southern hemisphere, and also stitch the regular hexagon around the south pole. Connect the zig zag lines, forming the sides of the pentagons and hexagons to complete the marking. Remove the waste thread S12 lines, but you may wish to be sure to keep the accurate north and south pole pins in place, depending on the needs of the design you plan to stitch. Additional lines may be added to any face to create a center point.