Calculators
Dodecagonal Bipyramid Calculator
Calculate centered dodecagonal bipyramid volume, twenty-four-face exterior surface area, and slant heights from a regular dodecagon side and two heights.
Measure two pyramids sharing a regular dodecagon.
Two pyramids share a regular dodecagon 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/12)); shared internal area B = 12ar/2; volume V = B(h₁ + h₂)/3. Face slant heights are ℓ₁ = hypot(h₁, r) and ℓ₂ = hypot(h₂, r). Exterior area A = 12a(ℓ₁ + ℓ₂)/2 includes twenty-four triangular faces and excludes the internal dodecagon. For a = 2 and both heights = 3, B ≈ 44.7846096908, V ≈ 89.5692193817 cubic units, and A ≈ 114.920168207 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 dodecagonal bipyramid volume calculated?
For regular dodecagon side a, B = 12a²/(4 tan(π/12)). Volume is B(h₁ + h₂)/3, where each height is perpendicular to the shared base plane.
Does exterior area include the dodecagon?
No. The shared dodecagon is internal. The twenty-four exterior triangles have total area 12a(ℓ₁ + ℓ₂)/2, where ℓ = √(h² + r²) and r = a/(2 tan(π/12)).
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.