(drawn with base edge length 1 and height 2)

face count | 10

volume | 2 h s^2 cot(π/8)≈4.82843 h s^2 lateral surface area | 8 h s base area | 2 s^2 cot(π/8)≈4.82843 s^2 surface area | 4 s (2 h + s cot(π/8))≈4 s (2 h + 2.41421 s) (assuming base edge length s and height h)