1. What is the Total Surface Area of Rhombicuboctahedron?

The Total Surface Area of a Rhombicuboctahedron is the total area of all its faces combined. A Rhombicuboctahedron is an Archimedean solid with 8 triangular and 18 square faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area of Rhombicuboctahedron (m²)
• \( r_c \) — Circumsphere Radius of Rhombicuboctahedron (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula calculates the total surface area based on the circumsphere radius of the Rhombicuboctahedron, using mathematical constants and geometric relationships.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is important in geometry, architecture, and material science for determining properties like material requirements, heat transfer, and structural analysis of polyhedral shapes.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid. The calculator will compute the total surface area using the derived formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 26 faces: 8 equilateral triangles and 18 squares.

Q2: What is the circumsphere radius?
A: The circumsphere radius is the radius of a sphere that passes through all vertices of the polyhedron.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first.

Q4: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places for accuracy.

Q5: Are there other ways to calculate surface area?
A: Yes, surface area can also be calculated using edge length or other geometric properties, but this calculator uses circumsphere radius as input.