| NAME |
TYPE |
Petrie |
multiplicity |
ORDER |
FACES |
VERTICES |
EDGES |
poss |
MODEL -- description |
Refs and models |
| Conder |
Tessel. |
length |
mV |
mF |
no mirr. |
# |
N-gons |
# |
Val |
# |
symm. |
|
|
| |
|
|
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|
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|
|
|
| R2.1 |
{3,8} |
12 |
2 |
1 |
48 |
16 |
3 |
6 |
8 |
24 |
D3 |
disk2, hos-3 -- four 3-claws + 12 horns |
WB1911, jjvw09,
|
| dual |
{8,3} |
12 |
1 |
2 |
|
6 |
8 |
16 |
3 |
24 |
D3 |
hos-3 -- six C-clamps |
jjvw09, |
| R2.2 |
{4,6} |
12 |
3 |
2 |
24 |
6 |
4 |
4 |
6 |
12 |
D3 |
hos-3 -- half-tubes |
chs08, jjvw09, |
| dual |
{6,4} |
12 |
2 |
3 |
|
4 |
6 |
6 |
4 |
12 |
D3 |
hos-3 -- 3-finger hands |
chs08, jjvw09, |
| R2.3 |
{4,8} |
8 |
8 |
2 |
16 |
4 |
4 |
2 |
8 |
8 |
D2 |
loop-2; stlk-2
|
chs09, jjvw09, chs10,
|
| dual |
{8,4} |
8 |
2 |
8 |
|
2 |
8 |
4 |
4 |
8 |
D2 |
loop-2; stlk-2
|
jjvw09, chs10,
|
| R2.4 |
{5,10} |
2 |
10 |
5 |
10 |
2 |
5 |
1 |
10 |
5 |
C2 |
stlk-2 -- V10 on top, 2 interlvd 5-claws |
chs09, chs09, |
| dual |
{10,5} |
2 |
5 |
10 |
|
1 |
10 |
2 |
5 |
5 |
C2 |
stlk-2 -- V5 on top and bottom |
chs09, chs09, |
| R2.5 - sd |
{6,6} |
2 |
6 |
6 |
12 |
2 |
6 |
2 |
6 |
6 |
D2,C3 |
hos-3 -- straight vertex-flower |
jjvw09, chs09, chs09,
|
| R2.6 - sd |
{8,8} |
2 |
8 |
8 |
8 |
1 |
8 |
1 |
8 |
4 |
C2 |
stlk-2 -- V8 on top |
jjvw09, chs09, chs09, |
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
| R3.1 |
{3,7} |
8 |
1 |
1 |
168 |
56 |
3 |
24 |
7 |
84 |
TETRA |
tetrus -- Klein |
FK1879, Will19??, chs06, |
| dual |
{7,3} |
8 |
|
|
|
24 |
7 |
56 |
3 |
84 |
TETRA |
tetrus -- Klein |
BT1993, HF1993, ES1994, chs06, jjvw09, |
| R3.2 |
{3,8} |
6 |
1 |
1 |
96 |
32 |
3 |
12 |
8 |
48 |
TETRA |
tetrus |
chs04, chs04, |
| dual |
{8,3} |
6 |
|
|
|
12 |
8 |
32 |
3 |
48 |
TETRA |
tetrus |
jjvw09, |
| R3.3 |
{3,12} |
6 |
4 |
1 |
48 |
16 |
3 |
4 |
12 |
24 |
D2,C3,C4 |
hos-4, but D2 symm. |
chs09, chs09, |
| dual |
{12,3} |
6 |
|
|
|
4 |
12 |
16 |
3 |
24 |
D2,C3,C4 |
hos-4, but D2 symm. |
chs09, |
| R3.4 |
{4,6} |
6 |
2 |
1 |
48 |
12 |
4 |
8 |
6 |
24 |
TET, D4
|
hos-4 |
chs09,
|
| dual |
{6,4} |
6 |
|
|
|
8 |
6 |
12 |
4 |
24 |
TET,D4 |
hos-4 |
chs09, chs09, jjvw09, |
| R3.5 |
{4,8} |
8 |
4 |
1 |
32 |
8 |
4 |
4 |
8 |
16 |
D2,C4 |
hos-4, but D2 symm. |
chs09, chs09, |
| dual |
{8,4} |
8 |
|
|
|
4 |
8 |
8 |
4 |
16 |
D2,C4 |
hos-4, but D2 symm. |
chs09, |
| R3.6 |
{4,8} |
8 |
4 |
2 |
32 |
8 |
4 |
4 |
8 |
16 |
D4 |
hos-4 |
chs08, |
| dual |
{8,4} |
8 |
|
|
|
4 |
8 |
8 |
4 |
16 |
D4 |
hos-4 |
chs08, |
| R3.7 |
{4,12} |
6 |
12 |
2 |
24 |
6 |
4 |
2 |
12 |
12 |
D3 |
loop-3 |
chs09, chs09,
|
| dual |
{12,4} |
6 |
|
|
|
2 |
12 |
6 |
4 |
12 |
D3 |
loop-3 |
jjvw09, chs09, chs09,
|
R3.8 - sd
|
{6,6} |
4 |
2 |
2 |
24 |
4 |
6 |
4 |
6 |
12 |
TETRA |
loop-3, tetrus |
jjvw09, chs09, |
| R3.9 |
{7,14} |
2 |
14 |
7 |
14 |
2 |
7 |
1 |
14 |
7 |
C2 |
stlk-3 -- V14 on top, 2 interlvd 7-claws |
chs09, |
| dual |
{14,7} |
2 |
|
|
|
1 |
14 |
2 |
7 |
7 |
C2 |
stlk-3 -- V7 on top and bottom |
chs09, |
| R3.10 - sd |
{8,8} |
4 |
8 |
8 |
16 |
2 |
8 |
2 |
8 |
8 |
D2,C4 |
hos-4 -- two V8 inside, twisted arms |
chs09, |
| R3.11 - sd |
{8,8} |
2 |
8 |
8 |
16 |
2 |
8 |
2 |
8 |
8 |
D2,C4 |
hos-4 -- straight vertex-flower |
jjvw09, chs09, chs09, |
| R3.12 - sd |
{12,12} |
2 |
12 |
12 |
12 |
1 |
12 |
1 |
12 |
6 |
C3 |
stlk-3 -- V12 on top |
chs09, chs09, chs09, chs09,
|
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
| R4.1 |
{3,12} |
6 |
3 |
1 |
72 |
24 |
3 |
6 |
12 |
36 |
OCTA |
octa + 4 tunnels
|
chs10, chs10, chs10,
|
| dual |
{12,3} |
6 |
|
|
|
6 |
12 |
24 |
3 |
36 |
OCTA |
octa + 4 tunnels |
chs10, chs10, chs10,
|
| R4.2 |
{4,5} |
6 |
1 |
1 |
120 |
30 |
4 |
24 |
5 |
60 |
OCTA |
octa + 4 tunnels |
chs07, chs10, chs10, |
| dual |
{5,4} |
6 |
|
|
|
24 |
5 |
30 |
4 |
60 |
OCTA |
octa + 4 tunnels |
chs10, chs10, chs10, |
| R4.3 |
{4,6} |
4 |
1 |
1 |
72 |
18 |
4 |
12 |
6 |
36 |
D3,D4 |
D3-stack |
chs10, chs10,
|
| dual |
{6,4} |
4 |
|
|
|
12 |
6 |
18 |
4 |
36 |
D3,D4 |
ThomsonG, D3-stack
|
jjvw09, chs10, |
| R4.4 |
{4,10} |
20 |
5 |
2 |
40 |
10 |
4 |
4 |
10 |
20 |
D5 |
hos-5 -- straight quads
|
chs08
|
| dual |
{10,4} |
20 |
|
|
|
4 |
10 |
10 |
4 |
20 |
D5 |
hos-5 -- 4 trunc. stars
|
chs08
|
| R4.5 |
{4,16} |
16 |
16 |
2 |
32 |
8 |
4 |
2 |
16 |
16 |
D2 |
loop-4; stlk-4
|
chs10, chs10,
|
| dual |
{16,4} |
16 |
|
|
|
2 |
16 |
8 |
4 |
16 |
D2 |
loop-4; stlk-4
|
chs10, chs10,
|
| R4.6 - sd |
{5,5} |
6 |
1 |
1 |
60 |
12 |
5 |
12 |
5 |
30 |
TETRA |
octa + 4 tunnels |
chs10, chs10, chs10,
|
| R4.7 - sd |
{6,6} |
6 |
3 |
3 |
36 |
6 |
6 |
6 |
6 |
18 |
D3 |
ThomsonG |
jjvw09, chs10, chs10, chs10,
|
| R4.8 |
{6,6} |
6 |
2 |
3 |
36 |
6 |
6 |
6 |
6 |
18 |
D3 |
torus + 3 arms
|
chs10, chs10,
|
| dual |
{6,6} |
6 |
|
|
|
6 |
6 |
6 |
6 |
18 |
D3 |
torus + 3 arms |
chs10, chs10,
|
| R4.9 |
{6,12} |
4 |
12 |
3 |
24 |
4 |
6 |
2 |
12 |
12 |
D4 |
disk-4 |
chs10, chs10, chs10, chs10,
|
| dual |
{12,6} |
4 |
|
|
|
2 |
12 |
4 |
6 |
12 |
D4 |
disk-4 |
chs10, chs10, |
| R4.10 |
{9,18} |
2 |
18 |
9 |
18 |
2 |
9 |
1 |
18 |
9 |
C3 |
stalk 4 -- V18 on top, 2 interlvd 9-claws
|
chs10, chs10, |
dual
|
{18,9} |
2 |
|
|
|
1 |
18 |
2 |
9 |
9 |
C3 |
stalk 4?
|
chs10, chs10, |
| R4.11 - sd |
{10,10} |
2 |
10 |
10 |
20 |
2 |
10 |
2 |
10 |
10 |
C5 |
hos-5 -- straight vertex-flower |
chs09, jjvw09,
|
| R4.12 - sd |
{16,16} |
2 |
16 |
16 |
16 |
1 |
16 |
1 |
16 |
8 |
C2 |
stlk-4 -- V16 on top |
jjvw09, chs09, chs09, |
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
| R5.1 |
{3,8} |
12 |
1 |
1 |
192 |
64 |
3 |
24 |
8 |
96 |
OCTA |
|
chs08, jjvw09,
|
| dual |
{8,3} |
12 |
|
|
|
24 |
8 |
64 |
3 |
96 |
OCTA |
cube |
chs08, jjvw09, |
| R5.2 |
{3,10} |
10 |
2 |
1 |
120 |
40 |
3 |
12 |
10 |
60 |
ICO?-TET |
|
chs10, |
| dual |
{10,3} |
10 |
|
|
|
12 |
10 |
40 |
3 |
60 |
ICO?-TET |
|
chs10,
|
| R5.3 |
{4,5} |
10 |
1 |
1 |
160 |
40 |
4 |
32 |
5 |
80 |
D5 |
|
chs10, |
| dual |
{5,4} |
10 |
|
|
|
32 |
5 |
40 |
4 |
80 |
D5 |
tor4-4 |
jjvw09, chs10, |
| R5.4 |
{4,6} |
12 |
1 |
1 |
96 |
24 |
4 |
16 |
6 |
48 |
OCTA |
|
chs08, |
| dual |
{6,4} |
12 |
|
|
|
16 |
6 |
24 |
4 |
48 |
OCTA |
cube |
chs08, jvw09, |
| R5.5 |
{4,8} |
4 |
2 |
1 |
64 |
16 |
4 |
8 |
8 |
32 |
D4 |
tor4-4, chain-loop
|
jjvw09, chs10, |
| dual |
{8,4} |
4 |
|
|
|
8 |
8 |
16 |
4 |
32 |
D4 |
chain-loop |
chs10, |
| R5.6 |
{4,8} |
8 |
2 |
2 |
64 |
16 |
4 |
8 |
8 |
32 |
D4 |
|
chs10, chs10, |
| dual |
{8,4} |
8 |
|
|
|
8 |
8 |
16 |
4 |
32 |
D4 |
|
chs10, |
| R5.7 |
{4,12} |
12 |
6 |
2 |
48 |
12 |
4 |
4 |
12 |
24 |
D6 |
|
chs08, |
| dual |
{12,4} |
12 |
|
|
|
4 |
12 |
12 |
4 |
24 |
D6 |
|
chs08,
|
| R5.8 |
{4,20} |
10 |
20 |
2 |
40 |
10 |
4 |
2 |
20 |
20 |
D5 |
|
chs10, |
| dual |
{20,4} |
10 |
|
|
|
2 |
20 |
10 |
4 |
20 |
D5 |
|
chs10, |
| R5.9 - sd |
{5,5} |
4 |
1 |
1 |
80 |
16 |
5 |
16 |
5 |
40 |
C5 |
|
chs10,
|
| R5.10 - sd |
{6,6} |
4 |
2 |
2 |
48 |
8 |
6 |
8 |
6 |
24 |
TETRA |
cube |
chs09, chs09, jjvw09,
|
| R5.11 |
{6,15} |
10 |
15 |
3 |
30 |
5 |
6 |
2 |
15 |
15 |
D5 |
stalk |
chs10, |
| dual |
{15,6} |
10 |
|
|
|
2 |
15 |
5 |
6 |
15 |
D5 |
|
|
| R5.12 - sd |
{8,8} |
4 |
4 |
4 |
32 |
4 |
8 |
4 |
8 |
16 |
D2 |
ring-chain |
jjvw09, chs10,
|
| R5.13 - sd |
{8,8} |
4 |
4 |
4 |
32 |
4 |
8 |
4 |
8 |
16 |
D2 |
ring-chain |
chs10, chs10, chs10, |
| R5.14 |
{11,22} |
2 |
22 |
11 |
22 |
2 |
11 |
1 |
22 |
11 |
C2 |
|
chs10, |
| dual |
{22,11} |
2 |
|
|
|
1 |
22 |
2 |
11 |
11 |
C2 |
|
|
| R5.15 - sd |
{12,12} |
2 |
12 |
12 |
24 |
2 |
12 |
2 |
12 |
12 |
C6 |
|
jjvw09, chs09,
|
| R5.16 - sd |
{20,20} |
2 |
20 |
20 |
20 |
1 |
20 |
1 |
20 |
10 |
C5 |
|
chs09, chs09, chs09,
|
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
| R7.1 |
{3,7} |
18 |
1 |
1 |
504 |
168 |
3 |
72 |
7 |
252 |
D7 |
|
chs10, chs10,
|
| dual |
{7,3} |
18 |
|
|
|
72 |
7 |
168 |
3 |
252 |
D7 |
disk7 |
chs10,
|
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