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Here is an animation of a cube with faces subdivided into two rectangles, morphing into a rhombic dodecahedron, with the Platonic dodecahedron as an intermediate state. This demonstrates that the e...
Answer
#4: Post edited
by
Alexei
·
2022-03-02T06:15:14Z (about 2 years ago)
removed useless reference to another user
[Here](https://i.pinimg.com/originals/b6/c9/65/b6c9653dcd8f47402bede44e1bc09398.gif) is an animation (Olin Lathrop, avert your eyes!) of a cube with faces subdivided into two rectangles, morphing into a rhombic dodecahedron, with the Platonic dodecahedron as an intermediate state. This demonstrates that the edge graph of the Platonic dodecahedron is the same as the edge graph of the subdivided cube.- There are probably a lot of ways you could generate this graph algorithmically, but here's one (in Python rather than pseudocode, but Python is pretty close to pseudocode):
- ```python
- edges = []
- for x, y, z in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
- for side in [0, 2]:
- a0 = {x: 0, y: 0, z: side}
- a1 = {x: 1, y: 0, z: side}
- a2 = {x: 2, y: 0, z: side}
- b0 = {x: 0, y: 2, z: side}
- b1 = {x: 1, y: 2, z: side}
- b2 = {x: 2, y: 2, z: side}
- edges.extend([(a0, a1), (a1, a2), (b0, b1), (b1, b2), (a1, b1)])
- ```
- [Here](https://i.pinimg.com/originals/b6/c9/65/b6c9653dcd8f47402bede44e1bc09398.gif) is an animation of a cube with faces subdivided into two rectangles, morphing into a rhombic dodecahedron, with the Platonic dodecahedron as an intermediate state. This demonstrates that the edge graph of the Platonic dodecahedron is the same as the edge graph of the subdivided cube.
- There are probably a lot of ways you could generate this graph algorithmically, but here's one (in Python rather than pseudocode, but Python is pretty close to pseudocode):
- ```python
- edges = []
- for x, y, z in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
- for side in [0, 2]:
- a0 = {x: 0, y: 0, z: side}
- a1 = {x: 1, y: 0, z: side}
- a2 = {x: 2, y: 0, z: side}
- b0 = {x: 0, y: 2, z: side}
- b1 = {x: 1, y: 2, z: side}
- b2 = {x: 2, y: 2, z: side}
- edges.extend([(a0, a1), (a1, a2), (b0, b1), (b1, b2), (a1, b1)])
- ```
#3: Post edited
by
r~~
·
2022-03-01T23:25:24Z (about 2 years ago)
- [Here](https://i.pinimg.com/originals/b6/c9/65/b6c9653dcd8f47402bede44e1bc09398.gif) is an animation (Olin Lathrop, avert your eyes!) of a cube with faces subdivided into two rectangles, morphing into a rhombic dodecahedron, with the Platonic dodecahedron as an intermediate state. This demonstrates that the edge graph of the Platonic dodecahedron is the same as the edge graph of the subdivided cube.
- There are probably a lot of ways you could generate this graph algorithmically, but here's one (in Python rather than pseudocode, but Python is pretty close to pseudocode):
- ```python
- edges = []
- for x, y, z in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
- for side in [0, 2]:
l0 = {x: 0, y: 0, z: side}l1 = {x: 1, y: 0, z: side}l2 = {x: 2, y: 0, z: side}r0 = {x: 0, y: 2, z: side}r1 = {x: 1, y: 2, z: side}r2 = {x: 2, y: 2, z: side}edges.extend([(l0, l1), (l1, l2), (r0, r1), (r1, r2), (l1, r1)])- ```
- [Here](https://i.pinimg.com/originals/b6/c9/65/b6c9653dcd8f47402bede44e1bc09398.gif) is an animation (Olin Lathrop, avert your eyes!) of a cube with faces subdivided into two rectangles, morphing into a rhombic dodecahedron, with the Platonic dodecahedron as an intermediate state. This demonstrates that the edge graph of the Platonic dodecahedron is the same as the edge graph of the subdivided cube.
- There are probably a lot of ways you could generate this graph algorithmically, but here's one (in Python rather than pseudocode, but Python is pretty close to pseudocode):
- ```python
- edges = []
- for x, y, z in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
- for side in [0, 2]:
- a0 = {x: 0, y: 0, z: side}
- a1 = {x: 1, y: 0, z: side}
- a2 = {x: 2, y: 0, z: side}
- b0 = {x: 0, y: 2, z: side}
- b1 = {x: 1, y: 2, z: side}
- b2 = {x: 2, y: 2, z: side}
- edges.extend([(a0, a1), (a1, a2), (b0, b1), (b1, b2), (a1, b1)])
- ```
#2: Post edited
by
r~~
·
2022-03-01T23:22:35Z (about 2 years ago)
- [Here](https://i.pinimg.com/originals/b6/c9/65/b6c9653dcd8f47402bede44e1bc09398.gif) is an animation (Olin Lathrop, avert your eyes!) of a cube with faces subdivided into two rectangles, morphing into a rhombic dodecahedron, with the Platonic dodecahedron as an intermediate state. This demonstrates that the edge graph of the Platonic dodecahedron is the same as the edge graph of the subdivided cube.
- There are probably a lot of ways you could generate this graph algorithmically, but here's one (in Python rather than pseudocode, but Python is pretty close to pseudocode):
- ```python
- edges = []
- for x, y, z in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
- for side in [0, 2]:
v01 = {x: 0, y: 0, z: side}v02 = {x: 1, y: 0, z: side}v03 = {x: 2, y: 0, z: side}v11 = {x: 0, y: 2, z: side}v12 = {x: 1, y: 2, z: side}v13 = {x: 2, y: 2, z: side}edges.extend([(v01, v02), (v02, v03), (v11, v12), (v12, v13), (v01, v11)])- ```
- [Here](https://i.pinimg.com/originals/b6/c9/65/b6c9653dcd8f47402bede44e1bc09398.gif) is an animation (Olin Lathrop, avert your eyes!) of a cube with faces subdivided into two rectangles, morphing into a rhombic dodecahedron, with the Platonic dodecahedron as an intermediate state. This demonstrates that the edge graph of the Platonic dodecahedron is the same as the edge graph of the subdivided cube.
- There are probably a lot of ways you could generate this graph algorithmically, but here's one (in Python rather than pseudocode, but Python is pretty close to pseudocode):
- ```python
- edges = []
- for x, y, z in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
- for side in [0, 2]:
- l0 = {x: 0, y: 0, z: side}
- l1 = {x: 1, y: 0, z: side}
- l2 = {x: 2, y: 0, z: side}
- r0 = {x: 0, y: 2, z: side}
- r1 = {x: 1, y: 2, z: side}
- r2 = {x: 2, y: 2, z: side}
- edges.extend([(l0, l1), (l1, l2), (r0, r1), (r1, r2), (l1, r1)])
- ```
#1: Initial revision
by
r~~
·
2022-03-01T22:25:43Z (about 2 years ago)
[Here](https://i.pinimg.com/originals/b6/c9/65/b6c9653dcd8f47402bede44e1bc09398.gif) is an animation (Olin Lathrop, avert your eyes!) of a cube with faces subdivided into two rectangles, morphing into a rhombic dodecahedron, with the Platonic dodecahedron as an intermediate state. This demonstrates that the edge graph of the Platonic dodecahedron is the same as the edge graph of the subdivided cube.
There are probably a lot of ways you could generate this graph algorithmically, but here's one (in Python rather than pseudocode, but Python is pretty close to pseudocode):
```python
edges = []
for x, y, z in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
for side in [0, 2]:
v01 = {x: 0, y: 0, z: side}
v02 = {x: 1, y: 0, z: side}
v03 = {x: 2, y: 0, z: side}
v11 = {x: 0, y: 2, z: side}
v12 = {x: 1, y: 2, z: side}
v13 = {x: 2, y: 2, z: side}
edges.extend([(v01, v02), (v02, v03), (v11, v12), (v12, v13), (v01, v11)])
```