Krystal Guo on Nostr: I think you're correct. As a graph theorist, though I maybe don't see the different ...

I think you're correct. As a graph theorist, though I maybe don't see the different between the icosahedron and the great icosahedron 😂

As a graph in SageMath, the icosahedron has 12 vertices and the neighbours are as follows:
0 [1, 5, 7, 8, 11]
1 [0, 2, 5, 6, 8]
2 [1, 3, 6, 8, 9]
3 [2, 4, 6, 9, 10]
4 [3, 5, 6, 10, 11]
5 [0, 1, 4, 6, 11]
6 [1, 2, 3, 4, 5]
7 [0, 8, 9, 10, 11]
8 [0, 1, 2, 7, 9]
9 [2, 3, 7, 8, 10]
10 [3, 4, 7, 9, 11]
11 [0, 4, 5, 7, 10]

Vertex positions version 1:
0: (1.0, 0.0, 0.0),
1: (0.0, 1.0, 0.0),
2: (0.0, 0.0, 1.0),
3: (-1.0, 0.0, 0.0),
4: (0.618034, 1.0, 0.618034),
5: (-1.0, -0.618034, 0.618034),
6: (0.618034, -0.618034, -1.0),
7: (-0.618034, 0.618034, 1.0),
8: (-0.618034, -1.0, -0.618034),
9: (1.0, 0.618034, -0.618034),
10: (0.0, -1.0, 0.0),
11: (0.0, 0.0, -1.0)
This produces a drawing of the great icosahedron. I scaled so that they are on the unit sphere and I've also plotted the unit sphere (in light blue), see attached video 1.

Vertex positions version 2:
0: [1, 0, 0],
1: [0, 1, 0],
2: [0, 0, 1],
3: [-1, 0, 0],
4: [-1.618034, 1, -1.618034],
5: [-1, 1.618034, -1.618034],
6: [-1.618034, 1.618034, -1],
7: [1.618034, -1.618034, 1],
8: [1.618034, -1, 1.618034],
9: [1, -1.618034, 1.618034],
10: [0, -1, 0],
11: [0, 0, -1]
This produces a drawing of the icosahedron, again scaled to be on the unit sphere (light blue), see attached video 2.