Acronym | quarn |
Name | quasirhombated penteract |
Circumradius | [3-sqrt(2)]/2 = 0.792893 |
Inradius wrt. qrit | (sqrt(2)-1)/2 = 0.207107 |
Inradius wrt. rap | sqrt[(43-30 sqrt(2))/20] = 0.169351 |
Inradius wrt. tepe | sqrt[(17-12 sqrt(2))/8] = 0.0606602 |
Coordinates | ((sqrt(2)-1)/2, (sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2, 1/2) & all permutations, all changes of sign |
Volume | [1205-843 sqrt(2)]/30 = 0.427266 |
Colonel of regiment | wavinant |
Dihedral angles
(at margins) | |
Face vector | 320, 1280, 1520, 680, 122 |
Confer |
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External links |
As abstract polytope quarn is isomorphic to sirn, thereby replacing querco by sirco and qrit by srit. – As such quarn is a lieutenant.
Incidence matrix according to Dynkin symbol
o3o3x3o4/3x . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 ------------+-----+---------+----------------+----------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 ------------+-----+---------+----------------+----------------+--------- . o3x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x | 4 | 2 2 | * * 480 * | 0 0 2 1 | 0 1 2 . . . o4/3x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 ------------+-----+---------+----------------+----------------+--------- o3o3x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x ♦ 6 | 6 3 | 2 0 3 0 | * * 320 * | 0 1 1 . . x3o4/3x ♦ 24 | 24 24 | 0 8 12 6 | * * * 40 | 0 0 2 ------------+-----+---------+----------------+----------------+--------- o3o3x3o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3x . x ♦ 8 | 12 4 | 8 0 6 0 | 2 0 4 0 | * 80 * . o3x3o4/3x ♦ 96 | 192 96 | 64 64 96 24 | 0 16 32 8 | * * 10
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