Klitzing wrote:Putting it all together, ...
The second type of variation is limited by ... P=2 for the second, where the polychora become dimensionally degenerate (becoming J51 and J57, resp. their prisms). Accordingly we have here the following bunch of valide CRFs:
...
oa3xo3oo xo&#zx = ope + 4 (alternate) trippies
oa3xo3xx xo&#zx = tuttip + 4 tripufs
xb3xo3oo xo&#zx = tuttip + 4 trippies
xb3xo3xx xo&#zx = tope + 4 (alternate) tripufs
(where a = (2+sqrt(10))/3 = 1.720759, b = a+x = 2.720759)
oa3xo4oo xo&#zx = cope + 6 cubpies
oa3xo4xx xo&#zx = ticcup + 6 (ortho) squipufs
xb3xo4oo xo&#zx = tope + 6 cubpies
xb3xo4xx xo&#zx = gircope + 6 (ortho) squipufs
(where a = w/q = 1.707107, b = a+x = 2.707107)
of3xo5oo xo&#zx = iddip + 12 peppies
of3xo5xx xo&#zx = tiddip + 12 (ortho) pepufs
xF3xo5oo xo&#zx = tipe + 12 peppies
xF3xo5xx xo&#zx = griddip + 12 (ortho) pepufs
(where F = ff = f+x)
...
Klitzing wrote:[...]
That is, this newly found CRF surely exists, whenever the 3D blend of waco (J86) and squippy (J1) would exist.
[...]
set A = polyroot(<-47, 494, -1119, -1808, 2128, 13696, 6112, -39680, -25600, 35328, 26880>, 0.2, 0.22)
set B = √(1 - A^2)
set C = √(2*(1 - 2*A))
set D = √(3 - 4*A^2)
set E = √(1 + A)
set F = 2*(1 - A)
# The two J89 cells
<±1, ±1, 2*B, ±1>
<±1, ±(1+2*A), 0, ±1>
<±(1 + C/√(1-A)), 0, -(2*A^2 + A - 1)/B, ±1>
<0, ±1, -D, ±1>
<±(D*C + E)/(F*E), 0, (2*A-1)*D/F - C/(F*E), ±1>
# The augment
<0, 0, 2*B + 1, 0>
Klitzing wrote:seems that username's find opened a box of pandorra!
select * from (
select p.name, f.id, f.degree, max(e.dihedral) m
from edge e, face f, lattice l, polyhedron p
where e.poly = p.id and f.poly=p.id and l.poly=p.id and
l.dim1=1 and l.id1=e.id and
l.dim2=2 and l.id2=f.id
group by p.id,f.id
order by p.id,f.id
)
where
(degree = 3 and m <= 114.094842552110691) or
(degree = 4 and m <= 135) or
(degree = 5 and m <= 166.717474411461012) or
(degree = 6 and m <= 114.094842552110691) or
(degree = 8 and m <= 135) or
(degree = 10 and m <= 166.717474411461012)
;
Klitzing wrote:Won't be besides of the squappip + 2 cubpy blend also a squappip + 2 squappy blend too?
Could someone check the according dihedrals?
[...]
$ aug_prisms show 20
[20] square antiprism:
[3] square (max 103.836°)
[4] square (max 103.836°)
$
o4o
x4o x4o -- x x4o (cube)
o4x o4x -- x o4x (gyro cube)
o4o
| |
| +-- s2s4s (squap)
+-------- s2s4s (squap)
x4o x4o -- x x4o (cube)
o4o o4o
o4x o4x -- x o4x (gyro cube)
| |
| +-- s2s4s (squap)
+-------- s2s4s (squap)
Klitzing wrote:[...]squappip + 2 squappy - blend[...]
As the base angle of the squappy is arccos[sqrt(sqrt(2))/2] = 53.515624°,
that of cubpy is 45°, and the cube-squap dihedral in squappip is 90°,
all 4 augmentations cannot be applied simultanuously, when restricting to CRFs.
mr_e_man wrote:Could 2n-prism || n-gon be called a pseudo-pyramid?
What is the reason for the term "magnabicupolic ring"? Why not just "bicupolic ring"?
quickfur wrote:mr_e_man wrote:Could 2n-prism || n-gon be called a pseudo-pyramid?
What is the reason for the term "magnabicupolic ring"? Why not just "bicupolic ring"?
It's historical. An n-gonal bicupolic ring is the same as 2n-gon||n-prism, whereas a magnabicupolic ring is 2n-prism||n-gon.
New Kid on the 4D analog of a Block wrote:I'm probably late to the party on this one, but could hexagonal/octagonal/decagonal prism cells of 3D-CRF prisms be augmented with triangular/square/pentagonal pucofastegia (K-4.51, 101, and 165, respectively)?
I don't even think I need to ask about antifastegia (K-4.6, 14, and 93, respectively), they don't look nearly shallow enough.
username5243 wrote:quickfur wrote:mr_e_man wrote:Could 2n-prism || n-gon be called a pseudo-pyramid?
What is the reason for the term "magnabicupolic ring"? Why not just "bicupolic ring"?
It's historical. An n-gonal bicupolic ring is the same as 2n-gon||n-prism, whereas a magnabicupolic ring is 2n-prism||n-gon.
2n-gon atop n-prism is orthobicupolic ring. There's also a gyrobicupolic ring that has an antiprism base instead.
Keiji wrote:As for the "reverse ortho" form, I like it Perhaps it should be called magna-something (in place of ortho/gyro-something), since we are inserting a larger polytope (octahedral prism as opposed to square (anti)prism), and magna is Latin for "great".
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