so it has three right cosets, each forming the vertices of an orthoplex inscribed in the 24-cell. So, we get **compound of three orthoplexes**: a way of partitioning the vertices of the 24-cell into those of three orthoplexes.

Second, look at the orthoplexes sitting inside the 600-cell! We’ve got 8-element subgroup of a 120-element group:

so it has 15 right cosets, each forming the vertices of an orthoplex inscribed in the 600-cell. So, we get a **compound of 15 orthoplexes**: a way of partitioning the vertices of the 600-cell into those of 15 orthoplexes.

And third, these fit nicely with what we saw last time: the 24-cells sitting inside the 600-cell! We saw a 24-element subgroup of a 120-element group

so it has 5 right cosets, each forming the vertices of a 24-cell inscribed in the 600-cell. That gave us the **compound of five 24-cells**: a way of partitioning the vertices of the 600-cell into those of five 24-cells.

Thanks! Now everyone can see what works and what doesn’t.

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here is the link text:

a normal link to just the animated gif here

and another try at an embedded img link:

]]>Pictures sometimes don’t show up when people other than me try to post them as comments here. I can add the animation if you tell me the link.

]]>as well as here with this animation:

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