Short Edge Of Deltoidal Icositetrahedron Given Total Surface Area Calculator

Formula Used:

\[ \text{Short Edge} = \frac{4+\sqrt{2}}{7} \times \sqrt{\frac{7 \times \text{Total Surface Area}}{12 \times \sqrt{61+38\sqrt{2}}}} \]

Short Edge of Deltoidal Icositetrahedron:

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1. What is the 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 this complex polyhedron. It is one of the key dimensional parameters used to characterize this geometric shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ \text{Short Edge} = \frac{4+\sqrt{2}}{7} \times \sqrt{\frac{7 \times \text{Total Surface Area}}{12 \times \sqrt{61+38\sqrt{2}}}} \]

Where:

\( \text{Total Surface Area} \) — The total surface area of the deltoidal icositetrahedron (m²)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula derives from the geometric properties of the deltoidal icositetrahedron and establishes the relationship between the total surface area and the length of the shortest edge.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is essential for understanding the dimensional proportions of the deltoidal icositetrahedron, which is important in various applications including crystallography, architectural design, and mathematical modeling of complex polyhedra.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding short edge length in meters.

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: Why are there different edge lengths in this polyhedron?
A: The deltoidal icositetrahedron has two types of edges - short edges and long edges, which creates its characteristic shape with deltoidal (kite-shaped) faces.

Q3: What are typical applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, crystallography, and mathematical research involving polyhedral structures.

Q4: How accurate is this formula?
A: The formula is mathematically exact for ideal deltoidal icositetrahedrons and provides precise calculations when correct input values are used.

Q5: Can this calculator handle different units?
A: The calculator uses square meters for surface area and meters for edge length. For other units, convert your measurements to these standard units before calculation.