Height of Tetragonal Trapezohedron Calculator

Height of Tetragonal Trapezohedron Formula:

\[ h = \sqrt{\frac{1}{2} \times (4 + 3 \times \sqrt{2})} \times l_{e(Antiprism)} \]

Height of Tetragonal Trapezohedron:

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1. What is the Height of Tetragonal Trapezohedron?

The Height of Tetragonal Trapezohedron is the distance between the two peak vertices where the long edges of Tetragonal Trapezohedron join. It is an important geometric measurement in crystallography and solid geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \sqrt{\frac{1}{2} \times (4 + 3 \times \sqrt{2})} \times l_{e(Antiprism)} \]

Where:

\( h \) — Height of Tetragonal Trapezohedron (m)
\( l_{e(Antiprism)} \) — Antiprism Edge Length of Tetragonal Trapezohedron (m)

Explanation: The formula calculates the height based on the antiprism edge length using a constant derived from geometric properties of the tetragonal trapezohedron.

3. Importance of Height Calculation

Details: Calculating the height of a tetragonal trapezohedron is important in crystallography, materials science, and geometric modeling for understanding the spatial dimensions and properties of this specific polyhedral form.

4. Using the Calculator

Tips: Enter the antiprism edge length in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a tetragonal trapezohedron?
A: A tetragonal trapezohedron is a polyhedron with eight faces, each of which is a kite. It is the dual polyhedron of a square antiprism.

Q2: What are the applications of this calculation?
A: This calculation is used in crystallography, mineralogy, and materials science where tetragonal trapezohedral structures occur, as well as in geometric modeling and 3D design.

Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect tetragonal trapezohedrons based on their geometric properties.

Q4: Can this calculator be used for other polyhedrons?
A: No, this specific formula applies only to tetragonal trapezohedrons. Other polyhedrons have different formulas for calculating height.

Q5: What units should I use for the input?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as long as you interpret the result in the same units.