Triangular:
365
(
365
+
1
)
2
=
365
×
366
2
=
133590
2
=
66795
{\textstyle {\frac {365(365+1)}{2}}={\frac {365\times 366}{2}}={\frac {133590}{2}}=66795}
Square:
365
2
=
133225
{\textstyle 365^{2}=133225}
Pentagonal:
3
(
365
2
)
−
365
2
=
399310
2
=
199655
{\textstyle {\frac {3(365^{2})-365}{2}}={\frac {399310}{2}}=199655}
Hexagonal:
365
(
2
(
365
)
−
1
)
=
266085
{\textstyle 365(2(365)-1)=266085}
Heptagonal:
5
(
365
2
)
−
3
(
365
)
2
=
665030
2
=
332515
{\textstyle {\frac {5(365^{2})-3(365)}{2}}={\frac {665030}{2}}=332515}
Octagonal:
3
(
365
2
)
−
2
(
365
)
=
398945
{\textstyle 3(365^{2})-2(365)=398945}
Nonagonal:
365
(
7
(
365
)
−
5
)
2
=
930750
2
=
465375
{\textstyle {\frac {365(7(365)-5)}{2}}={\frac {930750}{2}}=465375}
Decagonal:
4
(
365
2
)
−
3
(
365
)
=
531805
{\textstyle 4(365^{2})-3(365)=531805}
Dodecagonal:
5
(
365
2
)
−
4
(
365
)
=
664665
{\displaystyle 5(365^{2})-4(365)=664665}
Centered triangular:
3
(
365
2
)
+
3
(
365
)
+
2
2
=
400772
2
=
200386
{\textstyle {\frac {3(365^{2})+3(365)+2}{2}}={\frac {400772}{2}}=200386}
Centered square:
365
2
+
(
365
−
1
)
2
=
265721
{\textstyle 365^{2}+(365-1)^{2}=265721}
Centered pentagonal:
5
(
365
)
2
+
5
(
365
)
+
2
2
=
667952
2
=
333976
{\textstyle {\frac {5(365)^{2}+5(365)+2}{2}}={\frac {667952}{2}}=333976}
Centered hexagonal:
3
(
365
)
(
365
−
1
)
+
1
=
398581
{\textstyle 3(365)(365-1)+1=398581}
Centered heptagonal:
7
(
365
2
)
−
7
(
365
)
+
2
2
=
930022
2
=
465011
{\textstyle {\frac {7(365^{2})-7(365)+2}{2}}={\frac {930022}{2}}=465011}
Centered octaagonal:
(
2
(
365
)
−
1
)
2
=
531441
{\textstyle (2(365)-1)^{2}=531441}
Centered nonagonal:
(
3
(
365
)
−
2
)
(
3
(
365
)
−
1
)
2
=
1195742
2
=
597871
{\textstyle {\frac {(3(365)-2)(3(365)-1)}{2}}={\frac {1195742}{2}}=597871}
Centered decagonal:
5
(
365
)
2
+
5
(
365
)
+
1
=
667951
{\textstyle 5(365)^{2}+5(365)+1=667951}
Star:
6
(
365
)
(
365
−
1
)
+
1
=
797161
{\textstyle 6(365)(365-1)+1=797161}
Cube:
365
3
=
48627125
{\textstyle 365^{3}=48627125}
