Supported bilayer α-borophene (BL-α borophene) on Ag(111) substrate has been synthesized in recent experiments. Based on the experimentally observed quasi-planar C_6v B₃₆ (1), its monolayer assembly α⁺-borophene B₁₁ (P6/mmm) (2), and extensive global minimum searches augmented with density functional theory calculations, we predict herein freestanding BL-α⁺ borophenes B₂₂ (Cmmm) (3) and B₂₂ (C2/m) (4) which, as the most stable BL borophenes reported to date, are composed of interwoven boron triple chains as boron analogs of monolayer graphene (5) consisting of interwoven carbon single chains. The nearly degenerate eclipsed B₂₂ (3) and staggered B₂₂ (4) with the hexagonal hole density of η = 1/12 and interlayer bonding density of u = 1/4 appear to be two-dimensional semiconductors with the indirect band gaps of 0.952 and 1.144 eV, respectively. Detailed bonding analyses reveal one delocalized 12c-2e π bond over each hexagonal hole in both the B₂₂ (3) and B₂₂ (4), similar to the situation in monolayer graphene which contains one delocalized 6c-2e π bond over each C₆ hexagon. Furthermore, these BL-α⁺ borophenes appear to remain highly stable on Ag(111) substrate, presenting the possibility to form supported BL-α⁺ borophenes.