Armillary (hemi)sphere
armillary sphere - description

Polar gnomon is parallel to the Earth's axis. Dial is "wraped" around gnomon at equator plane.
While each side of equatorial dial is highlighted only for half a year, a dial of armillary sphere (or hemishpere) is highlighted all year long. Armillary sphere may additionally has tropic circles (North and South) and arctic circles. It will be a full skeletonized model of the Earth. For time reading halfshere is less confusing.

armillary sphere - calculations

Being the variety of equatorial sundials, armillary sphere may include the following important parallels:
1). North and South polar circles are the boundaries of the near-pole areas, where polar nigths and days occur (φ = ±(90°-23,5°)).
2). North and South tropics are the boundaries of the near-equator area, where Sun may be observed in zenith (φ = ±23,5°)).

armillary sphere - usage

Markup off armillary sphere is completely analogous to the marking of equatorial clocks, thus, all equal time intervals are marked with equal angles on the basis of relationship: one hour - 15°.
A hemispherical scale is very convinient for indicating different time scales. To indicate the difference between solar and mean time, polar gnomon can be made in the form of the analemma curve.