1. What is the Edge Length of Anticube?

The edge length of an anticube is defined as the length of the straight line joining two adjacent vertices of the anticube. An anticube (also known as a square antiprism) is a polyhedron that consists of two parallel square bases connected by an alternating band of triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge length of anticube (m)
• \( h \) — Height of anticube (m)
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the edge length of an anticube based on its height, using the geometric relationship between the height and edge length in a square antiprism structure.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is crucial for understanding the geometric properties of anticubes, designing structures with specific dimensions, and solving problems in geometry and 3D modeling.

4. Using the Calculator

Tips: Enter the height of the anticube in meters. The value must be positive and valid. The calculator will compute the corresponding edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is an anticube?
A: An anticube, also known as a square antiprism, is a polyhedron with two parallel square bases connected by an alternating band of triangles.

Q2: How is the edge length related to the height?
A: The edge length and height have a specific mathematical relationship defined by the geometry of the square antiprism structure.

Q3: What are the units for edge length?
A: The edge length is typically measured in meters (m), but the same formula works with any consistent unit system.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to square antiprisms (anticubes). Other polyhedra have different geometric relationships.

Q5: What if I know the edge length and want to find the height?
A: The formula can be rearranged to solve for height: \( h = l_e \times \sqrt{1 - \frac{1}{2 + \sqrt{2}}} \)