1. What is Height of Pentagonal Trapezohedron?

The Height of Pentagonal Trapezohedron is the vertical distance between two peak vertices where the long edges of the Pentagonal Trapezohedron join. It is an important geometric measurement for this three-dimensional shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( h \) — Height of Pentagonal Trapezohedron (m)
• \( le_{Long} \) — Long Edge of Pentagonal Trapezohedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

3. Formula Explanation

Details: The formula derives from the geometric properties of pentagonal trapezohedrons, incorporating the golden ratio (φ = (1+√5)/2) and the mathematical relationship between the long edge and the height of the shape.

4. Using the Calculator

Tips: Enter the length of the long edge in meters. The value must be positive and greater than zero. The calculator will compute the corresponding height of the pentagonal trapezohedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Trapezohedron?
A: A pentagonal trapezohedron is a polyhedron with ten faces, each being a kite shape, arranged in two pentagonal rings around the vertical axis.

Q2: What are the typical applications of this calculation?
A: This calculation is used in geometry, crystallography, and architectural design where pentagonal trapezohedral shapes are employed.

Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect pentagonal trapezohedrons and provides precise height calculations.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before input.

Q5: What if I get an error in calculation?
A: Ensure the input value is positive and numeric. The calculator requires valid numerical input greater than zero.