Eternity

Unfortunately the description of Eternity pieces is a breach of C.Monckton's copyright.
He does not wish the description of the pieces to be published in any form.

The pieces can be ordered and rotated in 209! 12^209 ways
209! 12^209 = 1.78 x 10^621 =
17833793934355021599464216158237055788952960455559
39664896828810374848966374425926802848828727014922
61315990512949829112824604442584684546438771083512
57522295775962865471757143571136280296815169246798
45693750081703198771035364248258740024533100467224
05456654075512366028886554451498575385935026198748
07077399743889281160970816002686003875771569106593
01735277688365076643732669480438110916866047044038
03926867875412469936614920088622123227132052495512
49471597235436985731148744631608948167694584536105
38446606237915444069558620656688440162999906372899
03387908414394356203520000000000000000000000000000
0000000000000000000000

Solution

unfortunately unknown ...
some attempts

Eternity-like puzzles

The set of 770 pieces I used.
Result no. 1
Result no. 2
Result no. 3 with small ATG part
(Another results are here by Brendan Owen and Mark Pursey)

Bigger puzzles

Dodecagons	"Squares"		Tiles
240 pieces 299 pieces 336 pieces 375 pieces 448 pieces 627 pieces	3 pieces 4 pieces 5 pieces 10 pieces 14 pieces 20 pieces 24 pieces	30 pieces 33 pieces 65 pieces 120 pieces 260 pieces	64 pieces * 192 pieces 260 pieces *

Statistics

# of sides	# of pieces in Eternity	%	# of pieces in 770 set	%
4	0	0	1	0.1
5	4	1.9	9	1.2
6	20	9.6	43	5.6
7	50	23.9	136	17.7
8	56	26.8	227	29.5
9	48	23.0	198	25.7
10	27	12.9	128	16.6
11	3	1.4	20	2.6
12	1	0.5	8	1.0
	209	100	770	100

# of angles > 180	# of pieces in Eternity	%	# of pieces in 770 set	%
0	4	1.9	11	1.4
1	59	28.2	150	19.5
2	103	49.2	387	50.2
3	39	18.7	201	26.1
4	4	1.9	21	2.8
	209	100	770	100

Against the grain

Few facts about Eternity :
1. The division of E pieces into triangles is unambiguous. ( This is not true for hexadudes. )
2. For every piece we can therefore decide whether it is aligned with uderlying grid. Pieces can go 'against the grain' in three different ways. I use three different colors for these pieces. ( some examples )
3. The boudaries of colored regions must be 'perpendicular'.

Parity

for explanation - Ed Pegg's page

Numbers of E pieces :

up/down parity	left/right parity	east/west parity
0 - 116 2 - 90 4 - 3	0 - 89 2 - 112 4 - 8	0 - 51 2 - 121 4 - 32 6 - 5

List of parities of E pieces

One attempt colored by parity - (balanced, plus two, plus four, plus six)
another one and the last one

Links

Ed Pegg Jr's Mathpuzzle.com
Brendan Owen's web page
Mark Pursey's web page

main page