1. What is Short Edge of Deltoidal Icositetrahedron?

The Short Edge of Deltoidal Icositetrahedron is the length of the shortest edge of the identical deltoidal faces that make up the Deltoidal Icositetrahedron, a Catalan solid with 24 congruent deltoidal faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere radius of the Deltoidal Icositetrahedron (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the shortest edge length based on the insphere radius, using the geometric properties of the Deltoidal Icositetrahedron.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is important for understanding the geometry of Deltoidal Icositetrahedron, its surface area, volume, and other geometric properties in mathematical and architectural applications.

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 Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 identical deltoidal faces, 26 vertices, and 48 edges.

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

Q3: Are there other edges in Deltoidal Icositetrahedron?
A: Yes, besides the short edge, there is also a long edge in each deltoidal face of the polyhedron.

Q4: What are typical applications of this calculation?
A: This calculation is used in geometry research, architectural design, and 3D modeling of complex polyhedra.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect Deltoidal Icositetrahedron, providing precise calculations based on geometric principles.