Kapemni

Wizipaŋ (parfleche) designs held important teachings, identity, and stories, linking makers to their heritage. Many of these items have triangle shapes, which are a common X-form called Kapemni in Dakota/Lakota (D/Lakota).
The X-form is a simply rendered symbol used to express complex ideas pervasive in religious iconography. It is often found embedded in more complex patterns in beadwork or painted objects such as [tipi]-painting. Many wizipaŋ also incorporate a diamond shape which were said to represent the breast of a turtle, a creature intimately connected with women’s sacred power in D/Lakota culture.
Ka-pemni (Pemni is ‘twisting;’ Ka is a prefix for a class of verbs whose action is performed by the wind) is used to symbolize the D/Lakotas’ entire relationship with the universe. It is an intertwining of the physical world, philosophy, and religion.

The triangle pointed up is the symbol for the earth (Unci Maka; Grandmother Earth; sacred earth), the triangle pointed down for the sun and stars (Tunkasila Skan; Grandfather Sky; sacred sky) while remaining one unit. It is through the power of their “sacred talk,” woglaka wakan (prayerful and mirrored dialogue), that the stars are created, the galaxies occur, and finally that all life on earth comes into being.
It is found in the conical shape of the tiphestola (tipi or home) as a place of nurturing, learning and growth. The cone-shaped, 3-dimensional symbol has two vortexes (two tipi shapes) joined at their apexes, and turning. It represents the power that carries prayer from below to above and the same power sent back down in response.
Kapemni represents the cosmology of reflection, a spiritual view in which the physical world is mirrored in the sky and stars. As above, so below.
For example, many Sacred Sites (like the Bdote, Wakaŋ Tipi & Hoǧáŋ Owáŋka Kiŋ in Minnesota; and Mato Tipila, Wind Cave & Black Elk Peak in South Dakota) have corresponding celestial features. The relationship between earthly locations and their positions in the sky are significant for many Indigenous peoples.