Truncated Cuboctahedron Edge Of Hexakis Octahedron Given Midsphere Radius Calculator

Formula Used:

\[ le(Truncated\ Cuboctahedron) = \frac{28 \times r_m}{(1 + (2 \times \sqrt{2})) \times 2 \times \sqrt{60 + (6 \times \sqrt{2})}} \]

Truncated Cuboctahedron Edge of Hexakis Octahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Truncated Cuboctahedron Edge of Hexakis Octahedron?

The Truncated Cuboctahedron Edge of Hexakis Octahedron is the length of the edges of a Hexakis Octahedron that is created by truncating the vertices of a Cuboctahedron. This geometric measurement is important in advanced polyhedral studies and mathematical modeling.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ le(Truncated\ Cuboctahedron) = \frac{28 \times r_m}{(1 + (2 \times \sqrt{2})) \times 2 \times \sqrt{60 + (6 \times \sqrt{2})}} \]

Where:

\( le(Truncated\ Cuboctahedron) \) — Truncated Cuboctahedron Edge of Hexakis Octahedron (m)
\( r_m \) — Midsphere Radius of Hexakis Octahedron (m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the edge length based on the midsphere radius using geometric relationships and mathematical constants derived from polyhedral geometry.

3. Importance of Calculation

Details: Accurate calculation of truncated cuboctahedron edges is crucial for geometric modeling, architectural design, crystallography studies, and advanced mathematical research involving polyhedral structures.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding truncated cuboctahedron edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid that is the dual of the truncated cuboctahedron, featuring 48 faces and 72 edges.

Q2: What is the significance of the midsphere radius?
A: The midsphere radius is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere.

Q3: What are typical values for these measurements?
A: Values vary significantly based on the scale of the polyhedron, but the relationship remains constant as defined by the formula.

Q4: Are there practical applications of this calculation?
A: Yes, in fields such as molecular modeling, architectural design, game development, and mathematical research involving complex polyhedra.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the geometric relationships defined by the formula, with accuracy limited only by computational precision.