This axe holder will be one flat loop around the belt,
and one oval loop around the axe shaft.

For the belt part, make two rectangles that's 7,5 cm by 8 cm.
For each part, bend it along the longer side and flatten,
then on the top, cut away the top 1,5 cm section from one
of the sides, and on the opposite side on the other rectangle.
You will now how two double-layered rectangles circa 4 cm wide
and 6 cm tall, with an extend of 1,5 cm on one of the layers.
Sew these close along the the open long side, and optionally,
decoratively on the closed long side. Next, sew them together
on the short sides, so the form a loop. The 1,5 cm extent should
be on the outer side, and arc over to the outer layer on the
other part. When done, you can remove excess material from the
extent.

Be sure to read the entire instructions before continuing!

For the axe part, you will make a X cm by 8 cm rectangle, where
X is the largest circumference around the axe's shaft (that was
12 cm in my case), plus at least 1 cm (that's a reallly snug fit,
you may want to add 2 cm instead). This part should also be bent
across the along the 8 cm side, to form a strap that's circa 4 cm
wide, and then sew along the longer side into a double-layered
piece. Then sew it together (on the short sides) so that it forms
a loop.

Next say, the two parts together, rotated 90 degrees relative
to eather other, so that one hole is horizontal and the other
vertical.

If you have a sheath, you have two, non-exclusive, options for
making it possible to attach it to the axe holder.

1) Add a half of a push button which a push button on the sheath,
   if it has one, can attach to. This push button half should
   be in the centre of the axe part, before it is bent and
   sew tohether, along the X side and centered on 2 cm from the
   edge on the 8 cm side (middle after it is bent into 4 cm).

2) Add an thin elastic strap going from one side of belt part
   over the axe part, to the other side of the belt part.
   (Center it) Being with only attach it one end. Then cover
   it with a single-layer (flat and thin) leather strap, then
   attach the other end. When covering the band, do not sew
   into it, instead sew across it.