1. What is the Gyroelongated Square Pyramid?

The Gyroelongated Square Pyramid is a Johnson solid formed by attaching a square antiprism to the base of a square pyramid. 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)
• \( h \) — Height of the Gyroelongated Square Pyramid (m)
• \( \sqrt{2} \) — Square root of 2 (≈1.4142)
• \( \sqrt{3} \) — Square root of 3 (≈1.7321)

Explanation: This formula calculates the total surface area based on the height of the gyroelongated square pyramid, accounting for all triangular and square faces.

3. Importance of TSA Calculation

Details: Calculating the total surface area is important for material estimation, structural analysis, and understanding the geometric properties of this complex polyhedron.

4. Using the Calculator

Tips: Enter the height of the gyroelongated square pyramid in meters. The height must be a positive value greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Johnson solid?
A: Johnson solids are convex polyhedra with regular faces that are not uniform (unlike Platonic or Archimedean 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, and mathematical research involving polyhedral geometry.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula is only applicable to gyroelongated square pyramids.

Q5: What units should be used for the height input?
A: The height should be entered in meters, and the result will be in square meters.