Height of Triakis Tetrahedron Given Volume Calculator

Height of Triakis Tetrahedron Formula:

\[ h = \frac{3}{5} \times \sqrt{6} \times \left( \frac{20 \times V}{3 \times \sqrt{2}} \right)^{\frac{1}{3}} \]

Height of Triakis Tetrahedron (h):

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1. What is the Height of Triakis Tetrahedron?

The height of a Triakis Tetrahedron is the vertical distance from any vertex to the opposite face. It's an important geometric measurement that helps characterize the three-dimensional shape of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{3}{5} \times \sqrt{6} \times \left( \frac{20 \times V}{3 \times \sqrt{2}} \right)^{\frac{1}{3}} \]

Where:

\( h \) — Height of Triakis Tetrahedron (m)
\( V \) — Volume of Triakis Tetrahedron (m³)
\( \sqrt{6} \) — Square root of 6
\( \sqrt{2} \) — Square root of 2

Explanation: This formula calculates the height of a Triakis Tetrahedron based on its volume, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Height Calculation

Details: Calculating the height of a Triakis Tetrahedron is essential for understanding its spatial dimensions, structural properties, and for applications in geometry, architecture, and material science.

4. Using the Calculator

Tips: Enter the volume of the Triakis Tetrahedron in cubic meters. The value must be positive and greater than zero for accurate 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: What are the units for height measurement?
A: The height is measured in meters (m), consistent with the volume input in cubic meters (m³).

Q3: Can this formula be used for irregular shapes?
A: No, this specific formula applies only to regular Triakis Tetrahedrons with equal edge lengths and symmetrical properties.

Q4: What is the relationship between volume and height?
A: The height increases with the cube root of the volume, meaning larger volumes result in proportionally smaller increases in height.

Q5: Are there practical applications of this calculation?
A: Yes, this calculation is useful in crystallography, architectural design, and any field dealing with polyhedral structures and their spatial properties.