Cool Banding!

This rock appears to be a type of jasper possibly a form with agate banding. Here are the characteristics that lead to this identification:

Coloration: The rock has a rich, warm coloration with shades of grey, purple, beige, and creme which are popular in jaspers due to iron oxide inclusions.
Translucency: Some parts of the rock are translucent, which is a common trait in agates. This translucency often comes from chalcedony, a form of silica.
Banding: The rock shows banding patterns, which are characteristic of agates where layers are formed by the deposition of silica from groundwater in cavities of volcanic rocks.
Texture: The surface appears somewhat polished, which is often done to enhance the natural beauty of agates and jaspers.

Given these features, it's likely that this rock is jasper. Agates are known for their fine grain and bright, contrasting colors, which aren't seen in this specimen.