Dr. Alexey Ignatchenko Research Group

Schwarzites. Names are composed of a letter for the TPMS type followed by the symmetry group, chemical element, and the number of atoms in the unit cell. Click on each name to explore 3D interactive model.
Entry # Name Crystal System Point symbol for net Density, g/cm3 Small chamber's neck
Large chamber's neck
Chirality Literature reference
1 P221-C168 cubic {4.7.8}4{6.7.8}2
{7.8^2}
0.905 (1111)^6 (2^8)^6 achiral 2025JOC
2 P207-C168g cubic {6^2.7} -- (2222)^6 (2^8)^6 chiral 2025JOC
3 P207-C168(P) cubic {6^2.7} 1.116 (2222)^6 (31313131)^6 chiral 2023JCC
4 P89-C168(M) tetragonal {6^2.7} 1.072 (2222)^2, (3131)^4 (2^6)^2, (32213221)^4 chiral 2025JOC
5 P130-C672 tetragonal {6^2.7} 1.186 (321321), (312312), (33121)^4 (31313131)^2, (4113221)^4 chiral 2023JCC
6 P197-C168(P) cubic {6^2.7} 1.552 (321321)^6 (321321)^6 chiral 2025JOC
7 P111-C168 tetragonal {6^2.7} 1.186 (411411)^4, (222222)^2 (312312)^2, (321321)^2, (32123212)^2 achiral 2025JOC
8 P75-C336 tetragonal {6^2.7} 1.184 (2222)^2, (3212)^4 (2^8)^2, (32222122)^4 chiral 2025JOC
9 P221-C216 cubic {6^2.7}7{6^3}2 1.017 -- (2^8)^6 achiral 2025JOC
10 P221-C312 cubic {6^2.7}7{6^3}6 0.939 -- (2^8)^6 achiral 2025JOC
11 P221-C456 cubic {6^2.7}7{6^3}12 0.758 -- (2^12)^6 achiral 2025JOC
12 P221-C408 cubic {6^2.7}7{6^3}10 0.85 -- (2^8)^6 achiral 2025JOC
13 P200-C276 cubic {6^2.7}14{6^3}9 0.958 (33113311)^6 -- achiral 2025JOC
14 P83-C200 tetragonal {6^2.7}21{6^3}4 1.069 (2222)^2, (322311)^4 (31313131)^2, (3131-1313)^4 achiral 2025JOC
15 P83-C216 tetragonal {6^2.7}7{6^3}2 1.012 (2222)^2, (322311)^4 -- achiral 2025JOC
16 P83-C184 tetragonal {6.7^2}{6^2.7}19
{6^3}3
1.145 -- (31313131)^2, (31131221)^4 achiral 2025JOC
17 P83-C224(P) tetragonal {6.7^2}{6^2.7}19
{6^3}8
1.019 -- -- achiral 2025JOC
18 P81-C240 tetragonal {6^2.7}7{6^3}3 0.943 -- -- meso 2025JOC
19 P195-C216(P) cubic {6^2.7}7{6^3}2 1.072 -- -- chiral 2025JOC
20 P195-C300(P) cubic {6^2.7}14{6^3}11 0.957 -- (312312)^6 chiral 2025JOC
21 P89-C1440 tetragonal {6^2.7}14{6^3} 1.155 (421421)^4 (22222222)^2, (31223122)^4, (22222222)^2 (421421)^4, (22222222)^2 4
dia
stereo
mers
2025JOC
22 P89-C192(P) tetragonal {6^2.7}7{6^3} 1.232 (31313131)^2, (42114211)^4 (42114211)^4, (22222222)^2 chiral 2025JOC
23 P207-C360(P) cubic {6^2.7}7{6^3}8 1.022 -- -- chiral 2025JOC
24 P221-C240 cubic {6^2.7}7{6^3}3 0.849 -- -- achiral (meso) 2025JOC
25 P221-C288 cubic {6^2.7}7{6^3}5 0.684 (2222)^6 (42114211)^6 achiral (meso) 2025JOC
26 P204-C216 cubic {6^2.7}7{6^3}2 1.084 (41124112)^6 (41124112)^6 achiral (meso) 2025JOC
27 P215-C192 cubic {6^2.7}7{6^3} 1.075 (411411)^6 (32123212)^6 achiral 2025JOC
28 P207-C288(M) cubic {6.7^2}{6^2.7}5
{6^3}6
0.954 (21212121)^6 -- chiral 2025JOC
29 P207-C216(M) cubic {6.7^2}{6^2.7}5
{6^3}3
1.097 (21212121)^6 -- chiral 2025JOC
30 P207-C144(M) cubic {6.7^2}{6^2.7}5 1.192 (21212121)^6 -- chiral 2025JOC
31 P207-C120(M) cubic {6.7^2}2{6^2.7}3 1.412 -- (2222)^6 chiral 2025JOC
32 P207-C56(1^8) cubic {6.8^2}3{6^2.8}3
{8^3}
-- (1111)^6 (11111111)^6 -- 2025JOC
33 P221-C56 cubic {6.8^2}3{6^2.8}3
{8^3}
1.724 (1111)^6 (2222)^6 achiral 2025JOC
34 P207-C56(2222)(P) cubic {7^3} 1.788 -- (2222)^6 chiral 2025JOC
35 P207-C80(P) cubic {6.7^2}3{6^2.7}3
{7^3}4
1.268 (1111)^6 (21212121)^6 chiral 2025JOC
36 P211-C32 cubic {8^3}



2017SC
37 P221-C120 cubic {6^2.8}4{6^3} 1.397 (2222)^6 (11111111)^6 achiral 2025JOC
38 P221-C192(1111) cubic {6.8^2}{6^2.8}2
{6^3}5
1.033 (1111)^6 -- achiral 2025JOC
39 P221-C192(2^8) cubic {6^2.9}3{6^3}5 1.059 (11111111)^6 (22222222)^6 achiral 2025JOC
40 D203-C672(M) cubic {6^2.7} 1.258 (313131)^4
-- chiral 1992PRL
41 D227-C768 cubic {6.7^2}2{6^2.7}3
{6^3}3
1.032 -- -- achiral 2025JOC
42 D227-C864(222) cubic {6^2.7}7{6^3}2 0.642 (222)^4 (332233223322)^4 achiral 2025JOC
43 D227-C864(222222) cubic {6^2.7}7{6^3}2 1.124 (222222)^4 (313131)^4 achiral 2025JOC
44 D227-C960 cubic {6^2.7}7{6^3}3 0.994 (313131)^4 (222222222)^4 achiral 2025JOC
45 D215-C960 cubic {6^2.7}7{6^3}3 1.084 (222222)^4
achiral 2025JOC
46 D227-C480 cubic {6.7^2}2{6^2.7}3 1.398 -- -- achiral 2025JOC
47 D227-C1248 cubic {6^2.7}7{6^3}6 0.873 (222222)^4 -- achiral 2025JOC
48 HT177-C252(313131)(P) hexagonal {6^2.7} 1.191 (313131)^2, (31313131)^3 (222222)^2, (2222)^6 chiral 2025JOC
49 HT177-C252(222)(P) hexagonal {6^2.7} 0.953 (222)^2, (2222)^3 (313131313131)^2, (31313131)^6 chiral 2025JOC
50 H149-C168(P) hexagonal {6^2.7} 1.277 (222222)^2, (321321)^3 -- chiral 2025JOC
51 H155-C558(P) hexagonal {6^2.7}28{6^3}3 1.226 (331331)^3 (321321)^3 chiral 2025JOC
52 GW182-C336(P) hexagonal {6^2.7} 1.275 (222222)^2, (321321)^3 -- chiral 2025JOC
53 GW156-C126 hexagonal {6.7.8}4{6^2.7}17 1.46 (32222)^2, open (313131)^2,
open
achiral 2025JOC
54 HT191-C288 hexagonal {6.7^2}{6^2.7}5{6^3}2 1.137 -- -- achiral 2025JOC
55 G199-C336(P) cubic {6^2.7} 1.292 -- -- chiral 2025JOC
56 IWP204-C576 cubic {6^2.7}7{6^3} 1.197 (313131)^8 (313131)^8 achiral 2025JOC
57 CLP93-C168 tetragonal {6^2.7} 1.141 (3131)^4, (31313131)^2 -- achiral 2025JOC
58 CLP131-C216 tetragonal {6^2.7}7{6^3}2 1.017 (2222)^4, (22222222)^2 -- achiral 2025JOC
59 CLP131-C312 tetragonal {6^2.7}7{6^3}6 0.948 (2222)^4, (22222222)^2 -- achiral 2025JOC
60 CLP66-C912 orthorhombic {6^2.7}7{6^3}12 0.824 (2222)^4, (22222222)^2
achiral 2025JOC
61 CLP115-C408 tetragonal {6^2.7}7{6^3}10 0.831 (222222)^4, (2^12)^2
achiral 2025JOC
62 CLP51-C816 orthorhombic {6^2.7}7{6^3}10 0.828 (2222)^4, (22222222)^2
achiral 2025JOC
63 CLP47-C264 triclinic {6^2.7}7{6^3}4 1.002 (2222)^4, (22222222)^2
achiral 2025JOC

Neck configuration shows the number of atoms in each heptagon (or a different polygon) composing a neck (the narrowest place where chambers connect). Each neck atom has one bond to connect to the opposite chamber. For example, configuration (222)^4 means that three polygons with 2 atoms in each polygon will be used to connect chamber's neck with another chamber and there are four necks in that chamber as illustrated below.

net example
                                with neck configuration (222)^4





TPMS