1. What is the Gyroelongated Square Pyramid?

The Gyroelongated Square Pyramid is a Johnson solid formed by attaching a square pyramid to a square antiprism. It has 13 faces: 12 equilateral triangles and 1 square.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area (m²)
• \( V \) — Volume of the Gyroelongated Square Pyramid (m³)
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the total surface area from the given volume using geometric relationships specific to the gyroelongated square pyramid.

3. Importance of TSA Calculation

Details: Calculating the total surface area is important for various applications including material estimation, heat transfer calculations, and structural analysis of this specific geometric shape.

4. Using the Calculator

Tips: Enter the volume in cubic meters. The volume must be a positive value greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Johnson solid?
A: Johnson solids are convex polyhedra with regular faces that are not uniform. There are 92 distinct Johnson solids.

Q2: How many faces does a gyroelongated square pyramid have?
A: It has 13 faces: 12 equilateral triangles and 1 square.

Q3: What are the practical applications of this calculation?
A: This calculation is useful in architecture, 3D modeling, material science, and educational contexts involving geometric shapes.

Q4: Are there limitations to this formula?
A: The formula is specifically designed for the gyroelongated square pyramid geometry and may not apply to other polyhedra.

Q5: Can this calculator handle very large volume values?
A: Yes, the calculator can handle a wide range of volume values, though extremely large values may be limited by computational precision.