Calculators

Heptagonal Bipyramid Calculator

Calculate centered heptagonal bipyramid volume, fourteen-face exterior surface area, and slant heights from a regular heptagon side and two heights.

Two pyramids share one regular heptagon base, with tips on opposite sides directly above and below its center. Enter the heptagon side and each perpendicular tip-to-base height in the same unit, from 1e-50 to 1e50. Exterior area includes 14 triangular faces and excludes the internal heptagon. All calculations stay in your browser.

Measure two pyramids sharing a regular heptagon.

Two pyramids share a regular heptagon 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/7)); shared internal area B = 7ar/2; volume V = B(h₁ + h₂)/3. Face slant heights are ℓ₁ = hypot(h₁, r) and ℓ₂ = hypot(h₂, r). Exterior area A = 7a(ℓ₁ + ℓ₂)/2 includes fourteen triangular faces and excludes the internal heptagon. For a = 2 and both heights = 3, B ≈ 14.535649776, V ≈ 29.071299552 cubic units, and A ≈ 51.0797460609 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 heptagonal bipyramid volume calculated?

For regular heptagon side a, B = 7a²/(4 tan(π/7)). Volume is B(h₁ + h₂)/3, where each height is perpendicular to the shared base plane.

Does exterior area include the heptagon?

No. The shared heptagon is internal. The fourteen exterior triangles have total area 7a(ℓ₁ + ℓ₂)/2, where ℓ = √(h² + r²) and r = a/(2 tan(π/7)).

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.