Polyhedron Dude wrote:Topax is the one with 6 garpops and 15 chopes.
Vertex Pattern:
a b
c g
h i
d e
f
6 * | 2 2 1 | 2 4 2 | 3 2 a
* 3 | 0 4 2 | 2 4 4 | 4 2 g
----+--------+--------+----
2 0 | 6 * * | 1 2 0 | 2 1 ae q
1 1 | * 12 * | 1 1 1 | 2 1 ag q
1 1 | * * 6 | 0 2 2 | 2 2 ai h
----+--------+--------+----
2 1 | 1 2 0 | 6 * * | 2 0 aeg qqq = verf(cube)
2 1 | 1 1 1 | * 12 * | 1 1 aeh qqh = verf(hip)
2 2 | 0 2 2 | * * 6 | 1 1 ahbi qh(-q)h = verf(cho)
----+--------+--------+----
3 2 | 2 4 2 | 2 2 1 | 6 * abfhi verf(chope)
4 2 | 2 4 4 | 0 4 2 | * 3 abdehi verf(garpop)
60 | 6 3 | 6 12 6 | 6 12 6 | 6 3
---+--------+-----------+----------+-----
2 | 180 * | 2 2 1 | 2 4 2 | 3 2
2 | * 90 | 0 4 2 | 2 4 4 | 4 2
---+--------+-----------+----------+-----
4 | 4 0 | 90 * * | 1 2 0 | 2 1
4 | 2 2 | * 180 * | 1 1 1 | 2 1
6 | 3 3 | * * 60 | 0 2 2 | 2 2
---+--------+-----------+----------+-----
8 | 8 4 | 2 4 0 | 45 * * | 2 0 cube
12 | 12 6 | 3 3 2 | * 60 * | 1 1 hip
12 | 12 12 | 0 6 4 | * * 30 | 1 1 cho
---+--------+-----------+----------+-----
24 | 36 24 | 12 24 8 | 6 4 2 | 15 * chope
30 | 60 30 | 15 30 20 | 0 10 5 | * 6 garpop
wendy wrote:We're evidently talking about Ft9 and Ft18 here. Two different things, really.
The first letter is the dimension, here A=1, B=2, ..., F=6. The second letter is the symmetry as per 3d (t=tetra, o=octahedron, c=cube, q=343, i=335, d=533.
The number is to be rendered in binary, and the nodes are numbered 1,2,4,8,16,&c, the nodes simply add. So ft9 is 3,3,3,3,3 with xoox marking, ie x3o3o3x3o3o. It's been mentioned before as a kind of short name.
Prism products are written by running the elements together, so a pentagonal prism is AB5.
?So, eg 3s0s0 (s=3 branch, nodes are numerical values). and 1s1s0 both have 0s0s1 (reversed tetrahedron)
Polyhedron Dude wrote:I now have all of the hoppic regiments counted...
Grand total - 923 plus 38 fissaries!
Klitzing wrote:Polyhedron Dude wrote:I now have all of the hoppic regiments counted...
Grand total - 923 plus 38 fissaries!
Congratulation! That's a new landmark!
And also named (incl. acronyms) them as well already?
--- rk
Polyhedron Dude wrote:Just finished sochax. Assuming no typos in my code, there are 1925 objects in the list!, one appears to be a pure compound, and I suspect many will be fissary. No IRCs should be on this list. Sochax is xoo8x and its verf is a -pen || rap, aka xooo || ooxo. Sochax is the 6-D version of siphin. This list excludes the 20 siphin fissaries and the one fissary in the spix regiment from its facet list, since these will lead only to fissaries. These regiments are starting to look scary.
polychoronlover wrote:The polyteron list is absolutely amazing!!! I was looking for Whytoffian members of regiments and I really wanted to know what the acronyms for some of them were, for example howoh, the cantellated hehad. Awesome!
240 | 8 2 | 4 4 4 8 1 | 2 2 2 4 4 4 | 1 2 2 2
----+---------+--------------------+---------------------+-----------
2 | 960 * | 1 1 1 1 0 | 1 1 1 1 1 1 | 1 1 1 1
2 | * 240 | 0 0 0 4 1 | 0 0 0 2 2 4 | 0 2 1 2
----+---------+--------------------+---------------------+-----------
3 | 3 0 | 320 * * * * | 1 1 0 1 0 0 | 1 0 1 1
3 | 3 0 | * 320 * * * | 0 1 1 0 0 1 | 1 1 0 1
4 | 4 0 | * * 240 * * | 1 0 1 0 1 0 | 1 1 1 0
4 | 2 2 | * * * 480 * | 0 0 0 1 1 1 | 0 1 1 1
3 | 0 3 | * * * * 80 | 0 0 0 0 0 4 | 0 2 0 2
----+---------+--------------------+---------------------+-----------
6 | 12 0 | 4 0 3 0 0 | 80 * * * * * | 1 0 1 0 thah
6 | 12 0 | 4 4 0 0 0 | * 80 * * * * | 1 0 0 1 oct
12 | 24 0 | 0 8 6 0 0 | * * 40 * * * | 1 1 0 0 co
6 | 6 3 | 2 0 0 3 0 | * * * 160 * * | 0 0 1 1 trip
8 | 8 4 | 0 0 2 4 0 | * * * * 120 * | 0 1 1 0 cube
12 | 12 12 | 0 4 0 6 4 | * * * * * 80 | 0 1 0 1 co
----+---------+--------------------+---------------------+-----------
24 | 96 0 | 32 32 24 0 0 | 8 8 4 0 0 0 | 10 * * * ratho
96 | 192 96 | 0 64 48 96 32 | 0 0 8 0 24 16 | * 5 * * rico
12 | 24 6 | 8 0 6 12 0 | 2 0 0 4 3 0 | * * 40 * thahp
30 | 60 30 | 20 20 0 30 10 | 0 5 0 10 0 5 | * * * 16 srip
For example, the operation x---o---o---x---x can be applied to:
o-...
/
x---o---o---o
\
o-...
resulting in:
x-...
/
x---o---o---x
\
x-...
Polyhedron Dude wrote:Later, I'll reveal how I come up with the 6-D regiment lists, its a fun yet grueling task with 8 tricky phases that are sort of like solving Sudoku puzzles, 'find all the triangles' puzzles, 'match lock and key' puzzles, and many more all rolled up into one.![]()
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o-3-o-3-o-3-o
3 3/2
o
o-3-o-3-o-3-o
3 3/2
o
o-3-o-3-o
3 3/23 3/2
o o
o-3-o-3-o
3 3/2
o-3-o
o
3 3/2
o-3-o
3 3
o3/2o
o
3
o--3--o--3--o
3 3/2
o
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