The atlas articulates with the axis. The atlas is the first cervical vertebra and articulates with the skull superiorly, and the axis (the second cervical vertebra) inferiorly. The joint between the atlas and axis, dubbed the atlanto-axial joint, is responsible for the increased range of motion of the skull (turning your head left/right, and nodding up/down).
The order of the atlas and axis can be remembered because, beginning from the skull, these two cervical vertebrae are in alphabetical order (aTlas then aXis).
The skull.
The Atlas
The condyles of the occipital bone articulate with the atlas.
No, doesn't articulate with any facial bones; only articulates with temporal bones of cranium.
Occipital condyles
occipital bone
The Hyoid bone does not have any articulations. It is commonly described as a gyroscope. It is held in place by the suprahyoid and infrahyoid musculature. It has a deep relationship with the Atlas however does not articulate directly with it.
none
The carpals articulate distally with the ulna. The carpals are also known as the wrist bones.
zyomatic
The ribs articulate with the thoracic vertebrae.
The cervical and lumbar vertebrae do not articulate with the ribs. The thoracic vertebrae are the only ones that articulate with the ribs.
Temporal