The Wave, Vermilion Cliffs Wilderness, Arizona. A hiker explores the cross-bedded sandstone formations in “The Wave” in the Coyote Buttes area of the Vermilion Cliffs Wilderness in northern Arizona. This region around the lower Paria River contains some of the most varied and spectacular formations of any location on the Colorado Plateau. The Vermilion Cliffs Wilderness of Arizona shares a common border with the Paria Canyons Wilderness of southern Utah. These two wilderness areas contain a maze of narrow canyons, windswept mesas, and countless hoodoos and pinnacles at the western edge of the Kaibab uplift.