Plane group packings

Densities of the densest plane group packings of regular convex n-gons obtained by the Entropic trust region packing algorithm. Each table entry contains a visualization of the packing configuration.

	3-gon	4-gon	5-gon	6-gon	7-gon	8-gon	9-gon	10-gon	11-gon	12-gon	13-gon	14-gon	15-gon	16-gon	17-gon	18-gon	19-gon	20-gon	21-gon	22-gon	23-gon	24-gon	25-gon	30-gon	36-gon	37-gon	39-gon	42-gon	55-gon	89-gon	Disc
p2	0.9999999	0.9999999	0.9213106	0.9999999	0.8926906	0.9061636	0.9010299	0.9137199	0.9076648	0.9282031	0.9043705	0.9074655	0.9047150	0.9090171	0.9069216	0.9162218	0.9059592	0.9073386	0.9057786	0.9078962	0.9068303	0.9121152	0.9064263	0.9102292	0.9092088	0.9067154	0.9065732	0.9085948	0.9068258	0.9068831	0.9068996
p2gg	0.9999999	0.9999999	0.9213106	0.9999999	0.8926906	0.9061636	0.8998911	0.9137199	0.9076648	0.9282032	0.9043705	0.9074655	0.9040306	0.9090171	0.9069216	0.9162218	0.9059592	0.9073386	0.9053663	0.9078962	0.9068303	0.9121152	0.9064263	0.9102292	0.9092088	0.9067154	0.9064331	0.9085948	0.9068258	0.9068831	0.9068996
pg	0.9999999	0.9999999	0.9213106	0.9999999	0.8926906	0.9061636	0.8986088	0.9137199	0.9076648	0.9282032	0.9043705	0.9074655	0.9023533	0.9090171	0.9069216	0.9162218	0.9059592	0.9073386	0.9052376	0.9078962	0.9068303	0.9121152	0.9064263	0.9102292	0.9092088	0.9067154	0.9064117	0.9085948	0.9068258	0.9068831	0.9068996
p3	0.6666666	0.7737684	0.8704800	0.9999999	0.8808500	0.8766506	0.8877354	0.8877506	0.8989629	0.9282032	0.9000514	0.8972213	0.9001741	0.8995067	0.9034831	0.9162218	0.9037971	0.9021808	0.9034922	0.9030030	0.9050054	0.9121152	0.9051366	0.9102292	0.9092088	0.9061077	0.9059168	0.9085948	0.9065451	0.9067687	0.9068996
p1	0.6666666	0.9999999	0.8172559	0.9999999	0.8601909	0.9061636	0.8877354	0.9137199	0.8891279	0.9282032	0.8938363	0.9074655	0.9001741	0.9090171	0.8994794	0.9162218	0.9008436	0.9073386	0.9034922	0.9078962	0.9028456	0.9121152	0.9034167	0.9102292	0.9092088	0.9053157	0.9059168	0.9085948	0.9061845	0.9066281	0.9068996
p2mg	0.9999999	0.9999999	0.8541019	0.8571428	0.8422610	0.8655534	0.8341984	0.8372213	0.8311609	0.8615612	0.8330633	0.8382375	0.8399388	0.8485635	0.8421519	0.8434670	0.8418991	0.8457107	0.8405228	0.8406806	0.8392954	0.8466283	0.8395230	0.8423912	0.8439306	0.8407669	0.8414747	0.8420952	0.8418053	0.8417961	0.8417872
cm	0.9999999	0.9999999	0.8541019	0.8571428	0.8422610	0.8655534	0.8341984	0.8372213	0.8279530	0.8615612	0.8321287	0.8382375	0.8399388	0.8485635	0.8421519	0.8434670	0.8418991	0.8457107	0.8405228	0.8406806	0.8386501	0.8466283	0.8391618	0.8423912	0.8439306	0.8405866	0.8414747	0.8420952	0.8418053	0.8417961	0.8417872
p4	0.7128127	0.9999999	0.8421137	0.8177689	0.8421945	0.8503106	0.8303053	0.8300404	0.8378042	0.8615612	0.8369105	0.8352788	0.8376586	0.8461384	0.8419033	0.8394577	0.8417746	0.8436777	0.8503106	0.8393389	0.8407273	0.8466283	0.8406152	0.8409576	0.8439306	0.8412738	0.8411836	0.8413652	0.8417912	0.8417900	0.8417872
p4gm	0.6961524	0.9999999	0.7111904	0.7461338	0.7647735	0.8284271	0.7659323	0.7720563	0.7762833	0.8038475	0.7766280	0.7786977	0.7802879	0.7956494	0.7804339	0.7813710	0.7821347	0.7919222	0.7822090	0.7827111	0.7831353	0.7899149	0.7831787	0.7839575	0.7873979	0.7844080	0.7845862	0.7846644	0.7849845	0.7852317	0.7853981
c2mm	0.6666666	0.9999999	0.7171403	0.7499999	0.7625321	0.8284271	0.7669742	0.7725424	0.7757096	0.8038475	0.7769742	0.7788232	0.7800620	0.7956494	0.7805888	0.7814167	0.7820237	0.7919222	0.7822918	0.7827316	0.7830728	0.7899149	0.7832274	0.7839634	0.7873979	0.7844231	0.7845734	0.7846659	0.7849799	0.7852328	0.7853981
pm	0.4999999	0.9999999	0.6909830	0.7499999	0.7382504	0.8284271	0.7571216	0.7725424	0.7665508	0.8038475	0.7719372	0.7788232	0.7753031	0.7956494	0.7775467	0.7814167	0.7791172	0.7919222	0.7802593	0.7827316	0.7811158	0.7899149	0.7817747	0.7839634	0.7873979	0.7837454	0.7839107	0.7846659	0.7846505	0.7851126	0.7853981
p2mm	0.4999999	0.9999999	0.6909830	0.7499999	0.7382504	0.8284271	0.7571216	0.7725424	0.7665508	0.8038475	0.7719372	0.7788232	0.7753031	0.7956494	0.7775467	0.7814167	0.7791172	0.7919222	0.7802593	0.7827316	0.7811158	0.7899149	0.7817747	0.7839634	0.7873979	0.7837454	0.7839107	0.7846659	0.7846505	0.7851126	0.7853981
p6	0.9999999	0.7219358	0.7593302	0.8571428	0.7574012	0.7643882	0.7853528	0.7693214	0.7729348	0.7956027	0.7725425	0.7732666	0.7799769	0.7742598	0.7753610	0.7853330	0.7752395	0.7753641	0.7786384	0.7757194	0.7762202	0.7818130	0.7761683	0.7801966	0.7793218	0.7768246	0.7777029	0.7787955	0.7771135	0.7772614	0.7773425
p31m	0.7499999	0.6632301	0.7016619	0.7199999	0.7208406	0.7156544	0.7341084	0.7165394	0.7218280	0.7461339	0.7220589	0.7238032	0.7308747	0.7258340	0.7273516	0.7282552	0.7278774	0.7269891	0.7299648	0.7266241	0.7272264	0.7332016	0.7272552	0.7287441	0.7308653	0.7282273	0.7292870	0.7288748	0.7288691	0.7289534	0.7290091
p3m1	0.9999999	0.4974226	0.5385407	0.6666666	0.5719655	0.5798083	0.6304149	0.5888775	0.5916426	0.6188021	0.5953579	0.5966415	0.6135979	0.5985185	0.5992167	0.6108145	0.6002951	0.6007165	0.6091508	0.6013927	0.6016664	0.6080768	0.6021181	0.6068195	0.6061392	0.6034684	0.6059109	0.6057298	0.6040880	0.6044044	0.6045997
p4mm	0.5773502	0.4999999	0.5553763	0.5214872	0.5144618	0.5685424	0.5244326	0.5331442	0.5424065	0.5358983	0.5414412	0.5360762	0.5338570	0.5460474	0.5350076	0.5372502	0.5401484	0.5379203	0.5399421	0.5378373	0.5368321	0.5421118	0.5371682	0.5383827	0.5386785	0.5393115	0.5382560	0.5386916	0.5386322	0.5388275	0.5390120
p6mm	0.4999999	0.4641016	0.4937279	0.4799999	0.4902521	0.4823532	0.4894056	0.4830540	0.4775021	0.4974226	0.4799512	0.4845448	0.4872498	0.4851838	0.4867589	0.4855035	0.4866096	0.4854864	0.4866432	0.4854253	0.4840900	0.4888010	0.4841886	0.4858294	0.4872435	0.4852676	0.4861913	0.4859165	0.4860784	0.4860337	0.4860060