1. What is Long Edge of Hexakis Icosahedron given Insphere Radius?

The Long Edge of Hexakis Icosahedron given Insphere Radius is a geometric calculation that determines the length of the longest edge of a Hexakis Icosahedron based on the radius of its inscribed sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Insphere Radius — Radius of the sphere inscribed within the Hexakis Icosahedron (m)

Explanation: This formula calculates the longest edge length of a Hexakis Icosahedron based on the radius of its inscribed sphere, using mathematical constants and geometric relationships.

3. Importance of Long Edge Calculation

Details: Calculating the long edge of a Hexakis Icosahedron is important in geometry, crystallography, and structural design where this polyhedral shape is used. It helps in understanding the spatial dimensions and proportions of the shape.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron, featuring 120 faces, 180 edges, and 62 vertices.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can fit inside the Hexakis Icosahedron, touching all its faces.

Q3: Are there other ways to calculate the long edge?
A: Yes, the long edge can also be calculated using other parameters such as medium edge, short edge, or volume of the Hexakis Icosahedron.

Q4: What are typical values for the long edge?
A: The long edge length varies depending on the size of the Hexakis Icosahedron, but it's typically the longest dimension of the polyhedron.

Q5: Where is this calculation used in real-world applications?
A: This calculation is used in mathematics education, geometric modeling, architectural design, and in fields that study polyhedral structures.