Spheres complètes

Points

maille

Parties de spheres

CN = 12

Coordination number

edge 1

edge 2

a = 1

b = 4 \; r=\sqrt{2}·a

b^2 = a^2 + a^2

diagonal b

r = \frac{\sqrt{2}}{4}·a

radius

sur les faces

aux sommets

Plan P d'une face

plan-2

Plan médian

a_{1}: x^(2) + y^(2) + z^(2) = 1 / 8
a_{2}: (x - 1)^(2) + y^(2) + z^(2) = 1 / 8
a_{3}: x^(2) + (y - 1)^(2) + z^(2) = 1 / 8
a_{4}: (x - 1)^(2) + (y - 1)^(2) + z^(2) = 1 / 8
a_{5}: x^(2) + y^(2) + (z - 1)^(2) = 1 / 8
a_{6}: x^(2) + (y - 1)^(2) + (z - 1)^(2) = 1 / 8
a_{7}: (x - 1)^(2) + (y - 1)^(2) + (z - 1)^(2) = 1 / 8
a_{8}: (x - 1)^(2) + y^(2) + (z - 1)^(2) = 1 / 8
b_{1}: (x - 1 / 2)^(2) + (y - 1 / 2)^(2) + z^(2) = 1 / 8
b_{2}: (x - 1 / 2)^(2) + y^(2) + (z - 1 / 2)^(2) = 1 / 8
b_{3}: x^(2) + (y - 1 / 2)^(2) + (z - 1 / 2)^(2) = 1 / 8
b_{4}: (x - 1 / 2)^(2) + (y - 1)^(2) + (z - 1 / 2)^(2) = 1 / 8
b_{5}: (x - 1)^(2) + (y - 1 / 2)^(2) + (z - 1 / 2)^(2) = 1 / 8
b_{6}: (x - 1 / 2)^(2) + (y - 1 / 2)^(2) + (z - 1)^(2) = 1 / 8
C_{1}: (0, 0, 0)
C_{2}: (0, 1, 0)
C_{3}: (1, 1, 0)
C_{4}: (1, 0, 0)
C_{5}: (0, 0, 1)
C_{6}: (0, 1, 1)
C_{7}: (1, 1, 1)
C_{8}: (1, 0, 1)
D_{1}: (1 / 2, 1 / 2, 0)
D_{2}: (1 / 2, 0, 1 / 2)
D_{3}: (0, 1 / 2, 1 / 2)
D_{4}: (1 / 2, 1, 1 / 2)
D_{5}: (1, 1 / 2, 1 / 2)
D_{6}: (1 / 2, 1 / 2, 1)
mostraresferas = false
mostrarpuntos = true
cubo, C_62, C_72, C_82, cara1, cara2, cara4, cara5, cara3, cara6, arista01, arista02, arista03, arista04, arista05, arista06, arista07, arista08, arista10, arista11, arista12, arista09 = Prism(C_{1}, C_{2}, C_{3}, C_{4}, C_{5})
mostrarcelda = true
e_1 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)), ((sqrt(2) / 4 * sin(i)) * sin(j)), (sqrt(2) / 4 * cos(j)), i, 0, π / 2, j, 0, π / 2)
e_2 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)), ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1, (sqrt(2) / 4 * cos(j)), i, ((-π)) / 2, 0, j, 0, π / 2)
e_3 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)) + 1, ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1, (sqrt(2) / 4 * cos(j)), i, π, (3 * π / 2), j, 0, π / 2)
e_4 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)) + 1, ((sqrt(2) / 4 * sin(i)) * sin(j)), (sqrt(2) / 4 * cos(j)), i, π / 2, π, j, 0, π / 2)
e_5 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)), ((sqrt(2) / 4 * sin(i)) * sin(j)), (sqrt(2) / 4 * cos(j)) + 1, i, π, (3 * π / 2), j, (-π), ((-π)) / 2)
e_6 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)), ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1, (sqrt(2) / 4 * cos(j)) + 1, i, π / 2, π, j, (-π), ((-π)) / 2)
e_7 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)) + 1, ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1, (sqrt(2) / 4 * cos(j)) + 1, i, 0, π / 2, j, (-π), ((-π)) / 2)
e_8 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)) + 1, ((sqrt(2) / 4 * sin(i)) * sin(j)), (sqrt(2) / 4 * cos(j)) + 1, i, ((-π)) / 2, 0, j, (-π), ((-π)) / 2)
P11: (sqrt(2) / 4, 0, 0)
P12: (0, sqrt(2) / 4, 0)
P13: (0, 0, sqrt(2) / 4)
P21: (0, 1 - sqrt(2) / 4, 0)
P22: (sqrt(2) / 4, 1, 0)
P23: (0, 1, sqrt(2) / 4)
P31: (1 - sqrt(2) / 4, 1, 0)
P32: (1, 1 - sqrt(2) / 4, 0)
P33: (1, 1, sqrt(2) / 4)
P41: (1, sqrt(2) / 4, 0)
P42: (1 - sqrt(2) / 4, 0, 0)
P43: (1, 0, sqrt(2) / 4)
P51: (sqrt(2) / 4, 0, 1)
P52: (0, sqrt(2) / 4, 1)
P53: (0, 0, 1 - sqrt(2) / 4)
P61: (0, 1 - sqrt(2) / 4, 1)
P62: (sqrt(2) / 4, 1, 1)
P63: (0, 1, 1 - sqrt(2) / 4)
P71: (1 - sqrt(2) / 4, 1, 1)
P72: (1, 1 - sqrt(2) / 4, 1)
P73: (1, 1, 1 - sqrt(2) / 4)
P81: (1, sqrt(2) / 4, 1)
P82: (1 - sqrt(2) / 4, 0, 1)
P83: (1, 0, 1 - sqrt(2) / 4)
s11 = CircleSector(C_{1}, P11, P13)
s12 = CircleSector(C_{1}, P13, P12)
s13 = CircleSector(C_{1}, P12, P11)
s21 = CircleSector(C_{2}, P21, P23)
s22 = CircleSector(C_{2}, P23, P22)
s23 = CircleSector(C_{2}, P22, P21)
s31 = CircleSector(C_{3}, P31, P33)
s32 = CircleSector(C_{3}, P33, P32)
s33 = CircleSector(C_{3}, P32, P31)
s41 = CircleSector(C_{4}, P41, P43)
s42 = CircleSector(C_{4}, P43, P42)
s43 = CircleSector(C_{4}, P42, P41)
s51 = CircleSector(C_{5}, P53, P51)
s52 = CircleSector(C_{5}, P52, P53)
s53 = CircleSector(C_{5}, P51, P52)
s61 = CircleSector(C_{6}, P63, P61)
s62 = CircleSector(C_{6}, P62, P63)
s63 = CircleSector(C_{6}, P61, P62)
s71 = CircleSector(C_{7}, P73, P71)
s72 = CircleSector(C_{7}, P72, P73)
s73 = CircleSector(C_{7}, P71, P72)
s81 = CircleSector(C_{8}, P83, P81)
s82 = CircleSector(C_{8}, P82, P83)
s83 = CircleSector(C_{8}, P81, P82)
f_1 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)) + 1 / 2, ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1 / 2, (sqrt(2) / 4 * cos(j)), i, 0, (2 * π), j, 0, π / 2)
f_2 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)) + 1 / 2, (sqrt(2) / 4 * cos(j)), ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1 / 2, i, 0, (2 * π), j, 0, π / 2)
f_3 = Surface((sqrt(2) / 4 * cos(j)), ((sqrt(2) / 4 * cos(i)) * sin(j)) + 1 / 2, ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1 / 2, i, 0, (2 * π), j, 0, π / 2)
f_4 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)) + 1 / 2, (sqrt(2) / 4 * cos(j)) + 1, ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1 / 2, i, 0, (2 * π), j, π / 2, π)
f_5 = Surface((sqrt(2) / 4 * cos(j)) + 1, ((sqrt(2) / 4 * cos(i)) * sin(j)) + 1 / 2, ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1 / 2, i, 0, (2 * π), j, π / 2, π)
f_6 = Surface(((sqrt(2) / 4 * cos(i)) * sin(j)) + 1 / 2, ((sqrt(2) / 4 * sin(i)) * sin(j)) + 1 / 2, (sqrt(2) / 4 * cos(j)) + 1, i, 0, (2 * π), j, π / 2, π)
v16 = Vector(D_{1}, D_{6})
v24 = Vector(D_{2}, D_{4})
v35 = Vector(D_{3}, D_{5})
t1 = Circle(D_{1}, sqrt(2) / 4, v16)
t2 = Circle(D_{2}, sqrt(2) / 4, v24)
t3 = Circle(D_{3}, sqrt(2) / 4, v35)
t4 = Circle(D_{4}, sqrt(2) / 4, v24)
t5 = Circle(D_{5}, sqrt(2) / 4, v35)
t6 = Circle(D_{6}, sqrt(2) / 4, v16)
mostrarpartes = true
IC000: (1, 1 / 2, 1 / 2)
IC001: (1 / 2, 1 / 2, 0)
IC002: (1 / 2, 0, 1 / 2)
IC003: (1 / 2, 1 / 2, 1)
IC004: (1 / 2, 1, 1 / 2)
IC005: (1, 0, 0)
IC006: (1, 0, 1)
IC007: (1, 1, 1)
IC008: (1, 1, 0)
IC009: (3 / 2, 1 / 2, 0)
IC010: (3 / 2, 0, 1 / 2)
IC011: (3 / 2, 1 / 2, 1)
IC012: (3 / 2, 1, 1 / 2)
i001 = Segment(IC000, IC001)
i002 = Segment(IC000, IC002)
i003 = Segment(IC000, IC003)
i004 = Segment(IC000, IC004)
i005 = Segment(IC000, IC005)
i006 = Segment(IC000, IC006)
i007 = Segment(IC000, IC007)
i008 = Segment(IC000, IC008)
i009 = Segment(IC000, IC009)
i010 = Segment(IC000, IC010)
i011 = Segment(IC000, IC011)
i012 = Segment(IC000, IC012)
mostrarindice = false
AR01: (0, 0, 0)
AR02: (1, 0, 0)
a1 = Segment(AR01, AR02)
AR03: (1, 0, 0)
AR04: (1, 0, 1)
a2 = Segment(AR03, AR04)
mostrararista1 = false
mostrararista2 = false
α = Angle(AR01, AR03, AR04)
tr, tr01, tr02, tr03 = Polygon(AR01, AR03, AR04)
B01: (0, 0, 0)
B02: (1, 0, 1)
b = Segment(B01, B02)
mostrardiagonalb = false
R01: (0, 0, 0)
R02: (1 / 4, 0, 1 / 4)
r = Segment(R01, R02)
mostrarradio = false
a = true
c = true
P = Plane(C_{7}, C_{6}, C_{2})
e = false
f: z = 0.5
g = true
d = Plane(D_{4}, D_{3}, D_{2})
h = false