Short Edge Of Pentagonal Hexecontahedron Given Insphere Radius Calculator

Formula Used:

\[ \text{Short Edge} = \frac{\text{Insphere Radius} \times 2}{\sqrt{\frac{1 + 0.4715756}{(1 - 0.4715756) \times (1 - 2 \times 0.4715756)}}} \]

Short Edge of Pentagonal Hexecontahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Short Edge of Pentagonal Hexecontahedron?

The Short Edge of Pentagonal Hexecontahedron is the length of the shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron. It is a fundamental geometric property of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Short Edge} = \frac{\text{Insphere Radius} \times 2}{\sqrt{\frac{1 + 0.4715756}{(1 - 0.4715756) \times (1 - 2 \times 0.4715756)}}} \]

Where:

Insphere Radius - The radius of the sphere contained by the Pentagonal Hexecontahedron
0.4715756 - A constant value specific to the geometry of Pentagonal Hexecontahedron

Explanation: This formula establishes the mathematical relationship between the insphere radius and the short edge length of the pentagonal hexecontahedron, using specific geometric constants.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is essential for understanding the geometric properties of pentagonal hexecontahedron, including its surface area, volume, and other dimensional characteristics. It's particularly important in crystallography, material science, and advanced geometry applications.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding short edge length of the pentagonal hexecontahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Hexecontahedron?
A: A pentagonal hexecontahedron is a complex polyhedron with 60 pentagonal faces. It is the dual polyhedron of the snub dodecahedron.

Q2: What is the significance of the constant 0.4715756?
A: This constant is derived from the specific geometric properties and trigonometric relationships within the pentagonal hexecontahedron structure.

Q3: Can this calculator be used for other polyhedra?
A: No, this specific formula and calculator are designed exclusively for the pentagonal hexecontahedron geometry.

Q4: What units should I use for the input?
A: The calculator uses meters as the unit of measurement, but you can use any consistent unit system as long as you maintain consistency throughout your calculations.

Q5: How accurate is this calculation?
A: The calculation provides theoretical geometric accuracy based on the mathematical relationships of the pentagonal hexecontahedron. The precision depends on the accuracy of the input value.