Orthohedra Dimensions: Identifying the Cubic Case in 3D Geometry

To determine which set of dimensions represents a cube, follow these steps:

• Step 1: Review each set of dimensions.
• Step 2: Check if all dimensions in a set are equal.

Now, let's evaluate each option:

Step 1: Analyze the given choices:
Choice 1: Dimensions $20, 7, 12$
Choice 2: Dimensions $7, 9, 15$
Choice 3: Dimensions $12, 12, 12$
Choice 4: Dimensions $8, 5, 6$

Step 2: Check for equality among dimensions in each choice:
- Choice 1: $20, 7, 12$ are all different. Not a cube.
- Choice 2: $7, 9, 15$ are all different. Not a cube.
- Choice 3: $12, 12, 12$ are all equal. This is a cube.
- Choice 4: $8, 5, 6$ are all different. Not a cube.

Therefore, the set of dimensions $12, 12, 12$ indicates a cube.

The correct answer is: $12,12,12$.