Calculators
Nonagonal Bipyramid Calculator
Calculate centered nonagonal bipyramid volume, eighteen-face exterior surface area, and slant heights from a regular nonagon side and two heights.
Measure two pyramids sharing a regular nonagon.
Two pyramids share a regular nonagon with tips on opposite sides directly above and below its center. Enter side a and perpendicular heights h₁ and h₂ in the same length unit. Apothem r = a/(2 tan(π/9)); shared internal area B = 9ar/2; volume V = B(h₁ + h₂)/3. Face slant heights are ℓ₁ = hypot(h₁, r) and ℓ₂ = hypot(h₂, r). Exterior area A = 9a(ℓ₁ + ℓ₂)/2 includes eighteen triangular faces and excludes the internal nonagon. For a = 2 and both heights = 3, B ≈ 24.7272967751, V ≈ 49.4545935502 cubic units, and A ≈ 73.2240180761 square units. Unequal heights are supported; irregular bases and off-center tips are outside this model. Use positive lengths from 1e-50 to 1e50; scientific notation is accepted. Results use browser floating-point arithmetic rounded to 12 significant digits. Inputs remain in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How is nonagonal bipyramid volume calculated?
For regular nonagon side a, B = 9a²/(4 tan(π/9)). Volume is B(h₁ + h₂)/3, where each height is perpendicular to the shared base plane.
Does exterior area include the nonagon?
No. The shared nonagon is internal. The eighteen exterior triangles have total area 9a(ℓ₁ + ℓ₂)/2, where ℓ = √(h² + r²) and r = a/(2 tan(π/9)).
Can the pyramid heights differ?
Yes. Both heights must be positive. The two tips must lie on opposite sides of the base on the perpendicular line through its center.
Which units and inputs are supported?
Use the same length unit for all three inputs. Area is in square units and volume in cubic units. Positive lengths from 1e-50 to 1e50 are accepted, including scientific notation. Results are rounded to 12 significant digits.
Does this require equilateral triangular faces?
No. The base must be regular and tips centered, but the triangular faces need not be equilateral. The two halves may have different heights.
Are my measurements uploaded?
No. Calculation, copying, and reset run locally in your browser.