I assume here that you are speaking of the sacred image of the Kiowa tribe in Momaday's The Way to Rainy Mountain (as, apart from the literary imagery in Momaday's work, that is the main image connected with this particular Native American tribe). To talk about this image is to talk about the second part of the myth the Kiowa tribe associates with creation: the Tai-me bundle. (The first part has to do with Talyi-da-i or "Boy Medicine" and the sons of the Sun god.) In short, the Tai-me image and effigy signify that the Kiowa culture is centered around the Sun.
Let us take a look at the second part of the Kiowa creation myth to learn how the Tai-me relates to this devout Native American tribe. The Crow comes as a messenger of the Sun so that the tribe can learn about the importance of their main deity. It is through the Crow that the Kiowa make friends with a strange creature: the Tai-me. The Tai-me is actually a strange mixture of bird and mammal. Because the creature comes from the sky and is related to both the Crow and the Sun, the Tai-me becomes the center of worship during the Kiowa Sun Dance. Tai-me eventually flies back to the Sun to remain unified, but vows to stay with the Kiowa tribe in the form of a stone image that you refer to in your question. This effigy is kept in a bundle and only unwrapped on one day a year when it is suspended on a pole in the Sun Dance lodge in order for the Kiowa to worship the effigy of Tai-me.
In conclusion, the strange creature-image of Tai-me shows that the Kiowa culture is certainly Sun-centered. Because the worship of the image of Tai-me is done during the Sun Dance, even this shows the Kiowa have the Sun as their central deity.