1. What is the Height of Triakis Tetrahedron given Surface to Volume Ratio?

The height of a Triakis Tetrahedron is the vertical distance from any vertex to the opposite face. This calculator determines the height based on the surface to volume ratio of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Triakis Tetrahedron (m)
• \( RA/V \) — Surface to Volume Ratio of Triakis Tetrahedron (1/m)
• \( \sqrt{33} \) — Square root of 33

Explanation: The formula calculates the height by dividing the constant term (12/5 × √33) by the surface to volume ratio.

3. Importance of Height Calculation

Details: Calculating the height of a Triakis Tetrahedron is important in geometry and 3D modeling applications where precise dimensional relationships are required.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be greater than 0 for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that can be constructed by attaching triangular pyramids to each face of a regular tetrahedron.

Q2: Why is the surface to volume ratio important?
A: The surface to volume ratio is an important geometric property that relates the external surface area to the internal volume of a 3D shape.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size and proportions of the specific Triakis Tetrahedron, with smaller objects having higher ratios.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Tetrahedron due to its unique geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Triakis Tetrahedron, assuming precise input values.