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Height of Anticube Given Volume Calculator

Height of Anticube Formula:

\[ h = \sqrt{1 - \frac{1}{2 + \sqrt{2}}} \times \left( \frac{3V}{\sqrt{1 + \sqrt{2}} \times \sqrt{2 + \sqrt{2}}} \right)^{\frac{1}{3}} \]

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1. What is the Height of Anticube?

The height of an anticube is defined as the measure of the vertical distance between the top and bottom square-shaped faces of the anticube. It is an important geometric parameter that helps characterize the three-dimensional structure of this unique polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ h = \sqrt{1 - \frac{1}{2 + \sqrt{2}}} \times \left( \frac{3V}{\sqrt{1 + \sqrt{2}} \times \sqrt{2 + \sqrt{2}}} \right)^{\frac{1}{3}} \]

Where:

Explanation: This formula derives from the geometric properties of anticubes, relating the height to the volume through mathematical constants and operations.

3. Importance of Height Calculation

Details: Calculating the height of an anticube is essential for understanding its spatial dimensions, structural properties, and for various applications in geometry, architecture, and 3D modeling.

4. Using the Calculator

Tips: Enter the volume of the anticube in cubic meters. The value must be positive and greater than zero. The calculator will compute the corresponding height.

5. Frequently Asked Questions (FAQ)

Q1: What is an anticube?
A: An anticube is a polyhedron that serves as the dual polyhedron of the square antiprism, featuring unique geometric properties.

Q2: What units should I use for volume input?
A: The calculator expects volume in cubic meters (m³). For other units, convert to cubic meters first.

Q3: How accurate is the calculation?
A: The calculation provides high mathematical accuracy based on the precise geometric formula for anticubes.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to anticubes due to their unique geometric properties.

Q5: What if I get an error in calculation?
A: Ensure you've entered a valid positive volume value. The calculation requires volume > 0.

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