  Topological metal/semimetals (TMs) have emerged as a new frontier in the
field of quantum materials. A few two-dimensional (2D) boron sheets have been
suggested as Dirac materials, however, to date TMs made of three-dimensional
(3D) boron structures have not been found. Herein, by means of systematic first
principles computations, we discovered that a rather stable 3D boron allotrope,
namely 3D-alpha' boron, is a nodal-chain semimetal. In the momentum space, six
nodal lines and rings contact each other and form a novel spindle nodal chain.
This 3D-alpha' boron can be formed by stacking 2D wiggle alpha' boron sheets,
which are also nodal-ring semimetals. In addition, our chemical bond analysis
revealed that the topological properties of the 3D and 2D boron structures are
related to the pi bonds between boron atoms, however, the bonding
characteristics are different from those in the 2D and 3D carbon structures.
