Volume Of Triakis Tetrahedron Given Pyramidal Edge Length Calculator

Volume Of Triakis Tetrahedron Formula:

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

Volume Of Triakis Tetrahedron (V):

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1. What is the Volume Of Triakis Tetrahedron?

The Volume Of Triakis Tetrahedron represents the quantity of three dimensional space enclosed by the entire surface of Triakis Tetrahedron. It is calculated based on the pyramidal edge length of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Triakis Tetrahedron (m³)
\( l_e \) — Pyramidal Edge Length of Triakis Tetrahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the volume by scaling the pyramidal edge length, cubing it, and applying geometric constants specific to the Triakis Tetrahedron shape.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for understanding the spatial properties of the Triakis Tetrahedron, material requirements, and various engineering applications involving this specific polyhedral shape.

4. Using the Calculator

Tips: Enter the pyramidal edge length in meters. The value must be positive and valid 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 seen as a tetrahedron with triangular pyramids added to each face.

Q2: How accurate is this formula?
A: The formula is mathematically exact for a perfect Triakis Tetrahedron shape with the given pyramidal edge length.

Q3: What units should be used for input?
A: The calculator uses meters as the default unit, but any consistent unit system can be used as long as the output volume is interpreted accordingly.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for more precise calculations.

Q5: What are practical applications of this calculation?
A: This calculation is useful in geometry, architecture, material science, and any field dealing with polyhedral structures and their volumetric properties.