Height of Triakis Tetrahedron Calculator

Height of Triakis Tetrahedron Formula:

\[ h = \frac{3\sqrt{6}}{5} \times l_{e(Tetrahedron)} \]

Height of Triakis Tetrahedron:

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1. What is the Height of Triakis Tetrahedron?

The Height of Triakis Tetrahedron is the vertical distance from any vertex of the Triakis Tetrahedron to the face which is directly opposite to that vertex. It is an important geometric measurement in three-dimensional space.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{3\sqrt{6}}{5} \times l_{e(Tetrahedron)} \]

Where:

\( h \) — Height of Triakis Tetrahedron (m)
\( l_{e(Tetrahedron)} \) — Tetrahedral Edge Length of Triakis Tetrahedron (m)
\( \sqrt{6} \) — Square root of 6 (approximately 2.44949)

Explanation: This formula calculates the height based on the tetrahedral edge length using a constant ratio derived from the geometric properties of the Triakis Tetrahedron.

3. Importance of Height Calculation

Details: Calculating the height of a Triakis Tetrahedron is essential for understanding its spatial dimensions, volume calculations, and for applications in geometry, architecture, and 3D modeling.

4. Using the Calculator

Tips: Enter the tetrahedral 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 constructed by attaching a triangular pyramid to each face of a regular tetrahedron.

Q2: What units should I use for the input?
A: The calculator uses meters as the default unit, but you can use any consistent unit as long as you maintain consistency throughout your calculations.

Q3: Can this formula be used for irregular tetrahedrons?
A: No, this formula is specifically for the regular Triakis Tetrahedron where all tetrahedral edges are equal in length.

Q4: What is the significance of the constant (3√6)/5?
A: This constant represents the fixed ratio between the height and the tetrahedral edge length in a regular Triakis Tetrahedron, derived from its geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect regular Triakis Tetrahedron, with accuracy limited only by the precision of your input values and computational rounding.