1. What is Circumsphere Radius of Great Stellated Dodecahedron?

The Circumsphere Radius of Great Stellated Dodecahedron is the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere. It is a fundamental geometric property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of Great Stellated Dodecahedron (m)
• \( h_{Pyramid} \) — Pyramidal Height of Great Stellated Dodecahedron (m)

Explanation: This formula establishes a direct linear relationship between the pyramidal height and the circumsphere radius of the Great Stellated Dodecahedron.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is crucial for understanding the spatial dimensions and geometric properties of the Great Stellated Dodecahedron, which is important in various mathematical and geometric applications.

4. Using the Calculator

Tips: Enter the pyramidal height in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Stellated Dodecahedron?
A: The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron, one of four regular non-convex polyhedra.

Q2: How is Pyramidal Height defined for this polyhedron?
A: Pyramidal Height refers to the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.

Q3: What are typical values for circumsphere radius?
A: The circumsphere radius depends on the size of the polyhedron and can vary significantly based on the pyramidal height.

Q4: Are there other methods to calculate circumsphere radius?
A: Yes, there are alternative geometric approaches, but this formula provides the most direct calculation when pyramidal height is known.

Q5: What applications use this calculation?
A: This calculation is primarily used in mathematical geometry, 3D modeling, and architectural design involving complex polyhedra.