Volume of Triakis Tetrahedron given Height Calculator

Formula:

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

Volume of Triakis Tetrahedron:

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1. What is the Volume of Triakis Tetrahedron?

The volume of a Triakis Tetrahedron is the quantity of three dimensional space enclosed by the entire surface of the polyhedron. It is a Catalan solid that can be constructed by attaching a triangular pyramid to each face of a regular tetrahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Triakis Tetrahedron (m³)
\( h \) — Height of Triakis Tetrahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{6} \) — Square root of 6 (approximately 2.4495)

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

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, architecture, and various scientific fields. It helps in understanding spatial relationships, material requirements, and structural properties.

4. Using the Calculator

Tips: Enter the height of the Triakis Tetrahedron in meters. The height must be a positive value greater than zero. The calculator will compute the volume using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that results from attaching a triangular pyramid to each face of a regular tetrahedron. It has 12 faces, 18 edges, and 8 vertices.

Q2: How is the height measured in a Triakis Tetrahedron?
A: The height is measured as the vertical distance from any vertex to the opposite face of the polyhedron.

Q3: What are the applications of volume calculation?
A: Volume calculations are used in various fields including architecture, engineering, manufacturing, and scientific research to determine capacity, material requirements, and spatial properties.

Q4: Are there other ways to calculate the volume?
A: Yes, the volume can also be calculated using edge length or other geometric properties, but the height-based formula provides a direct relationship between height and volume.

Q5: What units should be used for the calculation?
A: The calculator uses meters for input and cubic meters for output. Ensure consistent units for accurate results.