1. What is the Volume of Hexakis Octahedron?

The Hexakis Octahedron is a Catalan solid that is the dual of the truncated cuboctahedron. It has 48 faces, 72 edges, and 26 vertices. The volume calculation helps in understanding the spatial properties of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Hexakis Octahedron (m³)
• \( r_m \) — Midsphere Radius (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the volume based on the midsphere radius, incorporating mathematical constants and geometric relationships specific to the Hexakis Octahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including mathematics, engineering, architecture, and material science for understanding spatial properties and capacity.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will compute the volume using the precise mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid with 48 faces, 72 edges, and 26 vertices. It is the dual polyhedron of the truncated cuboctahedron.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: What are the applications of this calculation?
A: This calculation is used in geometry research, architectural design, material science, and 3D modeling applications.

Q4: How accurate is this formula?
A: The formula is mathematically exact for a perfect Hexakis Octahedron and provides precise volume calculations.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before calculation.