Pyramidal Edge Length Of Triakis Icosahedron Given Insphere Radius Calculator

Formula Used:

\[ l_{pyramid} = \frac{15 - \sqrt{5}}{22} \times \frac{4 \times r_i}{\sqrt{\frac{10 \times (33 + 13 \times \sqrt{5})}{61}}} \]

Pyramidal Edge Length (l_pyramid):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Pyramidal Edge Length of Triakis Icosahedron?

The Pyramidal Edge Length of Triakis Icosahedron refers to the length of the edges forming the pyramidal components of this polyhedron. The Triakis Icosahedron is a Catalan solid derived from the icosahedron by adding a pyramid on each face.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{pyramid} = \frac{15 - \sqrt{5}}{22} \times \frac{4 \times r_i}{\sqrt{\frac{10 \times (33 + 13 \times \sqrt{5})}{61}}} \]

Where:

\( l_{pyramid} \) — Pyramidal Edge Length (m)
\( r_i \) — Insphere Radius (m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the pyramidal edge length based on the insphere radius of the Triakis Icosahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Pyramidal Edge Length Calculation

Details: Calculating the pyramidal edge length is essential for understanding the geometric properties of the Triakis Icosahedron, including its surface area, volume, and other dimensional characteristics in mathematical and engineering applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that can be formed by adding a triangular pyramid to each face of a regular icosahedron, resulting in a polyhedron with 60 isosceles triangular faces.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can be contained within the Triakis Icosahedron, touching all its faces internally.

Q3: What are typical values for pyramidal edge length?
A: The pyramidal edge length varies depending on the size of the polyhedron. For standard-sized Triakis Icosahedrons, values typically range from a few centimeters to several meters in practical applications.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect Triakis Icosahedron geometry and may not account for manufacturing tolerances or material properties in physical implementations.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the Triakis Icosahedron only. Other polyhedra have different geometric relationships and require separate calculations.