Jonson qattiq moddalarining ro'yxati - List of Johnson solids

Yilda geometriya, a Jonson qattiq qat'iyan qavariq ko'pburchak, ularning har bir yuzi a muntazam ko'pburchak, lekin bu emas bir xil, ya'ni a emas Platonik qattiq, Arximed qattiq, prizma yoki antiprizm. 1966 yilda, Norman Jonson barcha 92 qattiq moddalarni o'z ichiga olgan ro'yxatni e'lon qildi va ularga ism va raqamlarini berdi. U faqat 92 kishi ekanligini isbotlamadi, ammo boshqalar yo'q deb taxmin qildi. Viktor Zalgaller 1969 yilda Jonsonning ro'yxati to'liq ekanligini isbotladi.

To'liq ro'yxat bu erda ustunlar bo'yicha saralash bilan. Taxminan muntazam tekislikli ko'pburchak yuzlari bo'lgan va norasmiy deb nomlangan boshqa ko'pburchaklarni qurish mumkin sog'indim Jonson qattiq; ularning aniq soni bo'lishi mumkin emas.

Jn	Qattiq ism	Tarmoq	Rasm	V	E	F	F3	F4	F5	F6	F8	F10	Simmetriya guruhi	Buyurtma
1	Kvadrat piramida			5	8	5	4	1					C4v, [4], (*44)	8
2	Besh burchakli piramida			6	10	6	5		1				C5v, [5], (*55)	10
3	Uchburchak kupa			9	15	8	4	3		1			C3v, [3], (*33)	6
4	Kvadrat kubogi			12	20	10	4	5			1		C4v, [4], (*44)	8
5	Besh burchakli kupe			15	25	12	5	5	1			1	C5v, [5], (*55)	10
6	Pentagonal rotunda			20	35	17	10		6			1	C5v, [5], (*55)	10
7	Uzaygan uchburchak piramida			7	12	7	4	3					C3v, [3], (*33)	6
8	Cho'zilgan kvadrat piramida			9	16	9	4	5					C4v, [4], (*44)	8
9	Cho'zilgan beshburchak piramida			11	20	11	5	5	1				C5v, [5], (*55)	10
10	Giro uzaytirilgan kvadrat piramida			9	20	13	12	1					C4v, [4], (*44)	8
11	Gyroelongated beshburchak piramida			11	25	16	15		1				C5v, [5], (*55)	10
12	Uchburchak bipiramida			5	9	6	6						D.3 soat, [3,2], (*223)	12
13	Besh qirrali bipiramida			7	15	10	10						D.5 soat, [5,2], (*225)	20
14	Uzaygan uchburchak bipiramida			8	15	9	6	3					D.3 soat, [3,2], (*223)	12
15	Cho'zilgan kvadrat bipiramida			10	20	12	8	4					D.4 soat, [4,2], (*224)	16
16	Cho'zilgan beshburchak bipiramida			12	25	15	10	5					D.5 soat, [5,2], (*225)	20
17	Gyroelongated kvadrat bipiramida			10	24	16	16						D.4d, [2+,8], (2*4)	16
18	Uzaygan uchburchak kubogi			15	27	14	4	9		1			C3v, [3], (*33)	6
19	Cho'zilgan kvadrat kubogi			20	36	18	4	13			1		C4v, [4], (*44)	8
20	Uzun bo'yli beshburchak kupe			25	45	22	5	15	1			1	C5v, [5], (*55)	10
21	Cho'zilgan beshburchak rotunda			30	55	27	10	10	6			1	C5v, [5], (*55)	10
22	Gyroelongated uchburchak kubogi			15	33	20	16	3		1			C3v, [3], (*33)	6
23	Gyroelongated kvadrat kubogi			20	44	26	20	5			1		C4v, [4], (*44)	8
24	Gyroelongated beshburchak kubogi			25	55	32	25	5	1			1	C5v, [5], (*55)	10
25	Gyroelongated beshburchak rotunda			30	65	37	30		6			1	C5v, [5], (*55)	10
26	Gyrobifastigium			8	14	8	4	4					D.2d, [2+,4], (2*2)	8
27	Uchburchak ortobikupola			12	24	14	8	6					D.3 soat, [3,2], (*223)	12
28	Kvadrat ortobikupola			16	32	18	8	10					D.4 soat, [4,2], (*224)	16
29	Kvadrat grobikupola			16	32	18	8	10					D.4d, [2+,8], (2*4)	16
30	Pentagonal ortobikupola			20	40	22	10	10	2				D.5 soat, [5,2], (*225)	20
31	Besh burchakli grobikupola			20	40	22	10	10	2				D.5d, [2+,10], (2*5)	20
32	Pentagonal ortokupolyarotunda			25	50	27	15	5	7				C5v, [5], (*55)	10
33	Pentagonal gyrokupolarotunda			25	50	27	15	5	7				C5v, [5], (*55)	10
34	Pentagonal orthobirotunda			30	60	32	20		12				D.5 soat, [5,2], (*225)	20
35	Uzaygan uchburchak ortobikupola			18	36	20	8	12					D.3 soat, [3,2], (*223)	12
36	Uzaygan uchburchak grobikupola			18	36	20	8	12					D.3d, [2+,6], (2*3)	12
37	Uzaygan kvadrat grobikupola			24	48	26	8	18					D.4d, [2+,8], (2*4)	16
38	Uzaygan beshburchak ortobikupola			30	60	32	10	20	2				D.5 soat, [5,2], (*225)	20
39	Cho'zilgan beshburchak grobikupola			30	60	32	10	20	2				D.5d, [2+,10], (2*5)	20
40	Uzaygan beshburchak ortokupolyarotunda			35	70	37	15	15	7				C5v, [5], (*55)	10
41	Uzaygan beshburchak gyrokupolarotunda			35	70	37	15	15	7				C5v, [5], (*55)	10
42	Uzaygan beshburchak ortobirotunda			40	80	42	20	10	12				D.5 soat, [5,2], (*225)	20
43	Cho'zilgan beshburchak girobirotunda			40	80	42	20	10	12				D.5d, [2+,10], (2*5)	20
44	Gyroelongated uchburchak bikupola			18	42	26	20	6					D.3, [3,2]+,(223)	6
45	Gyroelongated kvadrat bikupola			24	56	34	24	10					D.4, [4,2]+, (224)	8
46	Gyroelongated beshburchak bikupola			30	70	42	30	10	2				D.5, [5,2]+, (225)	10
47	Gyroelongated beshburchak kupolarotunda			35	80	47	35	5	7				C5, [5]+, (55)	5
48	Gyroelongated beshburchak birotunda			40	90	52	40		12				D.5, [5,2]+, (225)	10
49	Kattalashtirilgan uchburchak prizma			7	13	8	6	2					C2v, [2], (*22)	4
50	Ikki tomonlama uchburchak prizma			8	17	11	10	1					C2v, [2], (*22)	4
51	Uchburchak prizma			9	21	14	14						D.3 soat, [3,2], (*223)	12
52	Kattalashtirilgan beshburchak prizma			11	19	10	4	4	2				C2v, [2], (*22)	4
53	Ikki tomonlama beshburchak prizma			12	23	13	8	3	2				C2v, [2], (*22)	4
54	Kattalashtirilgan olti burchakli prizma			13	22	11	4	5		2			C2v, [2], (*22)	4
55	Parabiaugmented olti burchakli prizma			14	26	14	8	4		2			D.2 soat, [2,2], (*222)	8
56	Metabiaugmented olti burchakli prizma			14	26	14	8	4		2			C2v, [2], (*22)	4
57	Uchburchakli olti burchakli prizma			15	30	17	12	3		2			D.3 soat, [3,2], (*223)	12
58	Kattalashtirilgan dodekaedr			21	35	16	5		11				C5v, [5], (*55)	10
59	Parabiaugmented dodecahedron			22	40	20	10		10				D.5d, [2+,10], (2*5)	20
60	Metabiaugmented dodecahedron			22	40	20	10		10				C2v, [2], (*22)	4
61	Uchburchakli dodekaedr			23	45	24	15		9				C3v, [3], (*33)	6
62	Metabidiminatsiyalangan ikosaedr			10	20	12	10		2				C2v, [2], (*22)	4
63	Tridiminished icosahedr			9	15	8	5		3				C3v, [3], (*33)	6
64	Kattalashtirilgan trimined icosahedr			10	18	10	7		3				C3v, [3], (*33)	6
65	Kattalashtirilgan tetraedr			15	27	14	8	3		3			C3v, [3], (*33)	6
66	Kattalashtirilgan kesilgan kub			28	48	22	12	5			5		C4v, [4], (*44)	8
67	Biaugmented kesilgan kub			32	60	30	16	10			4		D.4 soat, [4,2], (*224)	16
68	Kattalashtirilgan qisqartirilgan dodekaedr			65	105	42	25	5	1			11	C5v, [5], (*55)	10
69	Parabiaugmented kesilgan dodekaedr			70	120	52	30	10	2			10	D.5d, [2+,10], (2*5)	20
70	Metabiaugmented kesilgan dodekaedr			70	120	52	30	10	2			10	C2v, [2], (*22)	4
71	Uchburchak kesilgan dodekaedr			75	135	62	35	15	3			9	C3v, [3], (*33)	6
72	Gyrate rombikosidodekaedr			60	120	62	20	30	12				C5v, [5], (*55)	10
73	Parabigirat rombikosidodekaedri			60	120	62	20	30	12				D.5d, [2+,10], (2*5)	20
74	Metabigirat rombikosidodekaedr			60	120	62	20	30	12				C2v, [2], (*22)	4
75	Rombikosidodekaedr trigrati			60	120	62	20	30	12				C3v, [3], (*33)	6
76	Kamaytirilgan rombikosidodekaedr			55	105	52	15	25	11			1	C5v, [5], (*55)	10
77	Paragirat kamaygan rombikosidodekaedr			55	105	52	15	25	11			1	C5v, [5], (*55)	10
78	Metagirat kamaygan rombikosidodekaedr			55	105	52	15	25	11			1	Cs, [ ], (*11)	2
79	Bigirat kamaygan rombikosidodekaedr			55	105	52	15	25	11			1	Cs, [ ], (*11)	2
80	Parabidiminatsiyalangan rombikosidodekaedr			50	90	42	10	20	10			2	D.5d, [2+,10], (2*5)	20
81	Metabidimekstirilgan rombikosidodekaedr			50	90	42	10	20	10			2	C2v, [2], (*22)	4
82	Gyrate rombikosidodekaedrni taklif qildi			50	90	42	10	20	10			2	Cs, [ ], (*11)	2
83	Trimimikosidodekaedr			45	75	32	5	15	9			3	C3v, [3], (*33)	6
84	Yengil dishenoid			8	18	12	12						D.2d, [2+,4], (2*2)	8
85	Snub kvadrat antiprizmi			16	40	26	24	2					D.4d, [2+,8], (2*4)	16
86	Sfenokorona			10	22	14	12	2					C2v, [2], (*22)	4
87	Kattalashtirilgan sfenokorona			11	26	17	16	1					Cs, [ ], (*11)	2
88	Sphenomegacorona			12	28	18	16	2					C2v, [2], (*22)	4
89	Hebesphenomegacorona			14	33	21	18	3					C2v, [2], (*22)	4
90	Dissenokingulum			16	38	24	20	4					D.2d, [2+,4], (2*2)	8
91	Bilunabirotunda			14	26	14	8	2	4				D.2 soat, [2,2], (*222)	8
92	Uchburchak hebesfenorotunda			18	36	20	13	3	3	1			C3v, [3], (*33)	6

orqaga tepaga Afsona:

• J_n - Jonsonning qattiq raqami
• Tarmoq - tekislangan (ochilmagan) tasvir
• V - Vertices soni
• E - qirralarning soni
• F - yuzlar soni (jami)
• F₃-F₁₀ - Yuzlar sonini yonma-yon hisoblash

Adabiyotlar

• Norman W. Jonson, "Doimiy yuzli qavariq qattiq moddalar", Kanada matematik jurnali, 18, 1966, 169–200 betlar. 92 ta qattiq moddalarning asl ro'yxati va boshqalar yo'q degan taxminni o'z ichiga oladi.
• Viktor A. Zalgaller (1969). Doimiy yuzlar bilan qavariq polyhedra. Maslahatchilar byurosi. ISBN yo'q. Jonsonning atigi 92 ta qattiq moddasi borligining birinchi dalili.

Tashqi havolalar

• Silveyn Gagnon "Doimiy yuzlari bilan konveks polyhedra^{[doimiy o'lik havola ]}", Strukturaviy topologiya, № 6, 1982, 83-95.
• Jonson qattiq moddalari Jorj V. Xart tomonidan.
• Bir sahifada turkumlangan barcha 92 ta qattiq jismlarning rasmlari
• Vayshteyn, Erik V. "Jonson Solid". MathWorld.
• Jonson Solidlarning VRML modellari Jim McNeill tomonidan
• Jonson Solidlarning VRML modellari Vladimir Bulatov tomonidan