Acronym | iddip, K-4.90 |
Name | icosidodecahedron prism |
Segmentochoron display | |
Cross sections |
© |
Circumradius | sqrt[7+2 sqrt(5)]/2 = 1.693527 |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles | |
Face vector | 60, 150, 124, 34 |
Confer |
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External links |
As abstract polytope iddip is isomorphic to giddip, thereby replacing id by gid and pip by stip.
Incidence matrix according to Dynkin symbol
x o3x5o . . . . | 60 | 1 4 | 4 2 2 | 2 2 1 --------+----+--------+----------+-------- x . . . | 2 | 30 * | 4 0 0 | 2 2 0 . . x . | 2 | * 120 | 1 1 1 | 1 1 1 --------+----+--------+----------+-------- x . x . | 4 | 2 2 | 60 * * | 1 1 0 . o3x . | 3 | 0 3 | * 40 * | 1 0 1 . . x5o | 5 | 0 5 | * * 24 | 0 1 1 --------+----+--------+----------+-------- x o3x . ♦ 6 | 3 6 | 3 2 0 | 20 * * x . x5o ♦ 10 | 5 10 | 5 0 2 | * 12 * . o3x5o ♦ 30 | 0 60 | 0 20 12 | * * 2
x o3x5/4o . . . . | 60 | 1 4 | 4 2 2 | 2 2 1 ----------+----+--------+----------+-------- x . . . | 2 | 30 * | 4 0 0 | 2 2 0 . . x . | 2 | * 120 | 1 1 1 | 1 1 1 ----------+----+--------+----------+-------- x . x . | 4 | 2 2 | 60 * * | 1 1 0 . o3x . | 3 | 0 3 | * 40 * | 1 0 1 . . x5/4o | 5 | 0 5 | * * 24 | 0 1 1 ----------+----+--------+----------+-------- x o3x . ♦ 6 | 3 6 | 3 2 0 | 20 * * x . x5/4o ♦ 10 | 5 10 | 5 0 2 | * 12 * . o3x5/4o ♦ 30 | 0 60 | 0 20 12 | * * 2
x o3/2x5o . . . . | 60 | 1 4 | 4 2 2 | 2 2 1 ----------+----+--------+----------+-------- x . . . | 2 | 30 * | 4 0 0 | 2 2 0 . . x . | 2 | * 120 | 1 1 1 | 1 1 1 ----------+----+--------+----------+-------- x . x . | 4 | 2 2 | 60 * * | 1 1 0 . o3/2x . | 3 | 0 3 | * 40 * | 1 0 1 . . x5o | 5 | 0 5 | * * 24 | 0 1 1 ----------+----+--------+----------+-------- x o3/2x . ♦ 6 | 3 6 | 3 2 0 | 20 * * x . x5o ♦ 10 | 5 10 | 5 0 2 | * 12 * . o3/2x5o ♦ 30 | 0 60 | 0 20 12 | * * 2
x o3/2x5/4o . . . . | 60 | 1 4 | 4 2 2 | 2 2 1 ------------+----+--------+----------+-------- x . . . | 2 | 30 * | 4 0 0 | 2 2 0 . . x . | 2 | * 120 | 1 1 1 | 1 1 1 ------------+----+--------+----------+-------- x . x . | 4 | 2 2 | 60 * * | 1 1 0 . o3/2x . | 3 | 0 3 | * 40 * | 1 0 1 . . x5/4o | 5 | 0 5 | * * 24 | 0 1 1 ------------+----+--------+----------+-------- x o3/2x . ♦ 6 | 3 6 | 3 2 0 | 20 * * x . x5/4o ♦ 10 | 5 10 | 5 0 2 | * 12 * . o3/2x5/4o ♦ 30 | 0 60 | 0 20 12 | * * 2
oo3xx5oo&#x → height = 1
(id || id)
o.3o.5o. | 30 * | 4 1 0 | 2 2 4 0 0 | 1 2 2 0
.o3.o5.o | * 30 | 0 1 4 | 0 0 4 2 2 | 0 2 2 1
------------+-------+----------+----------------+----------
.. x. .. | 2 0 | 60 * * | 1 1 1 0 0 | 1 1 1 0
oo3oo5oo&#x | 1 1 | * 30 * | 0 0 4 0 0 | 0 2 2 0
.. .x .. | 0 2 | * * 60 | 0 0 1 1 1 | 0 1 1 1
------------+-------+----------+----------------+----------
o.3x. .. | 3 0 | 3 0 0 | 20 * * * * | 1 1 0 0
.. x.5o. | 5 0 | 5 0 0 | * 12 * * * | 1 0 1 0
.. xx ..&#x | 2 2 | 1 2 1 | * * 60 * * | 0 1 1 0
.o3.x .. | 0 3 | 0 0 3 | * * * 20 * | 0 1 0 1
.. .x5.o | 0 5 | 0 0 5 | * * * * 12 | 0 0 1 1
------------+-------+----------+----------------+----------
o.3x.5o. ♦ 30 0 | 60 0 0 | 20 12 0 0 0 | 1 * * *
oo3xx ..&#x ♦ 3 3 | 3 3 3 | 1 0 3 1 0 | * 20 * *
.. xx5oo&#x ♦ 5 5 | 5 5 5 | 0 1 5 0 1 | * * 12 *
.o3.x5.o ♦ 0 30 | 0 0 60 | 0 0 0 20 12 | * * * 1
xxxxx xoxfo5ofxox&#xt → outer heights = sqrt[(5-sqrt(5))/10] = 0.525731 inner heights = sqrt[(5+sqrt(5))/10] = 0.850651 (pip || pseudo dual f-pip || pseudo dip || pseudo f-pip || dual pip) o.... o....5o.... | 10 * * * * | 1 2 2 0 0 0 0 0 0 0 0 0 0 | 2 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 1 0 0 0 0 0 .o... .o...5.o... | * 10 * * * | 0 0 2 1 2 0 0 0 0 0 0 0 0 | 0 0 2 1 2 2 1 0 0 0 0 0 0 0 0 0 | 0 1 2 1 1 0 0 0 0 ..o.. ..o..5..o.. | * * 20 * * | 0 0 0 0 1 1 1 1 1 0 0 0 0 | 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 | 0 0 1 1 1 1 1 0 0 ...o. ...o.5...o. | * * * 10 * | 0 0 0 0 0 0 0 0 2 1 2 0 0 | 0 0 0 0 0 0 0 0 0 2 2 1 2 1 0 0 | 0 0 0 1 0 2 1 1 0 ....o ....o5....o | * * * * 10 | 0 0 0 0 0 0 0 0 0 0 2 1 2 | 0 0 0 0 0 0 0 0 0 0 1 0 2 2 2 1 | 0 0 0 1 0 1 0 2 1 ----------------------+----------------+------------------------------------+-------------------------------------------+------------------ x.... ..... ..... | 2 0 0 0 0 | 5 * * * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 ..... x.... ..... | 2 0 0 0 0 | * 10 * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 0 0 0 oo... oo...5oo...&#x | 1 1 0 0 0 | * * 20 * * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0 .x... ..... ..... | 0 2 0 0 0 | * * * 5 * * * * * * * * * | 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 | 0 1 2 0 1 0 0 0 0 .oo.. .oo..5.oo..&#x | 0 1 1 0 0 | * * * * 20 * * * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 0 0 ..x.. ..... ..... | 0 0 2 0 0 | * * * * * 10 * * * * * * * | 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 | 0 0 1 0 1 1 1 0 0 ..... ..x.. ..... | 0 0 2 0 0 | * * * * * * 10 * * * * * * | 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 | 0 0 0 1 1 1 0 0 0 ..... ..... ..x.. | 0 0 2 0 0 | * * * * * * * 10 * * * * * | 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 | 0 0 1 1 0 0 1 0 0 ..oo. ..oo.5..oo.&#x | 0 0 1 1 0 | * * * * * * * * 20 * * * * | 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 0 1 0 1 1 0 0 ...x. ..... ..... | 0 0 0 2 0 | * * * * * * * * * 5 * * * | 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 | 0 0 0 0 0 2 1 1 0 ...oo ...oo5...oo&#x | 0 0 0 1 1 | * * * * * * * * * * 20 * * | 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 | 0 0 0 1 0 1 0 1 0 ....x ..... ..... | 0 0 0 0 2 | * * * * * * * * * * * 5 * | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 | 0 0 0 0 0 1 0 2 1 ..... ..... ....x | 0 0 0 0 2 | * * * * * * * * * * * * 10 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 1 0 0 0 1 1 ----------------------+----------------+------------------------------------+-------------------------------------------+------------------ x.... x.... ..... | 4 0 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 0 0 | 5 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 ..... x....5o.... | 5 0 0 0 0 | 0 5 0 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 xx... ..... .....&#x | 2 2 0 0 0 | 1 0 2 1 0 0 0 0 0 0 0 0 0 | * * 10 * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 ..... xo... .....&#x | 2 1 0 0 0 | 0 1 2 0 0 0 0 0 0 0 0 0 0 | * * * 10 * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 ..... ..... ofx..&#xt | 1 2 2 0 0 | 0 0 2 0 2 0 0 1 0 0 0 0 0 | * * * * 10 * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 .xx.. ..... .....&#x | 0 2 2 0 0 | 0 0 0 1 2 1 0 0 0 0 0 0 0 | * * * * * 10 * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 ..... .ox.. .....&#x | 0 1 2 0 0 | 0 0 0 0 2 0 1 0 0 0 0 0 0 | * * * * * * 10 * * * * * * * * * | 0 0 0 1 1 0 0 0 0 ..x.. ..x.. ..... | 0 0 4 0 0 | 0 0 0 0 0 2 2 0 0 0 0 0 0 | * * * * * * * 5 * * * * * * * * | 0 0 0 0 1 1 0 0 0 ..x.. ..... ..x.. | 0 0 4 0 0 | 0 0 0 0 0 2 0 2 0 0 0 0 0 | * * * * * * * * 5 * * * * * * * | 0 0 1 0 0 0 1 0 0 ..xx. ..... .....&#x | 0 0 2 2 0 | 0 0 0 0 0 1 0 0 2 1 0 0 0 | * * * * * * * * * 10 * * * * * * | 0 0 0 0 0 1 1 0 0 ..... ..xfo .....&#xt | 0 0 2 2 1 | 0 0 0 0 0 0 1 0 2 0 2 0 0 | * * * * * * * * * * 10 * * * * * | 0 0 0 1 0 1 0 0 0 ..... ..... ..xo.&#x | 0 0 2 1 0 | 0 0 0 0 0 0 0 1 2 0 0 0 0 | * * * * * * * * * * * 10 * * * * | 0 0 0 1 0 0 1 0 0 ...xx ..... .....&#x | 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 1 2 1 0 | * * * * * * * * * * * * 10 * * * | 0 0 0 0 0 1 0 1 0 ..... ..... ...ox&#x | 0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * * * 10 * * | 0 0 0 1 0 0 0 1 0 ....x ..... ....x | 0 0 0 0 4 | 0 0 0 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * 5 * | 0 0 0 0 0 0 0 1 1 ..... ....o5....x | 0 0 0 0 5 | 0 0 0 0 0 0 0 0 0 0 0 0 5 | * * * * * * * * * * * * * * * 2 | 0 0 0 1 0 0 0 0 1 ----------------------+----------------+------------------------------------+-------------------------------------------+------------------ x.... x....5o.... ♦ 10 0 0 0 0 | 5 10 0 0 0 0 0 0 0 0 0 0 0 | 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * xx... xo... .....&#x ♦ 4 2 0 0 0 | 2 2 4 1 0 0 0 0 0 0 0 0 0 | 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 | * 5 * * * * * * * xxx.. ..... ofx..&#xt ♦ 2 4 4 0 0 | 1 0 4 2 4 2 0 2 0 0 0 0 0 | 0 0 2 0 2 2 0 0 1 0 0 0 0 0 0 0 | * * 5 * * * * * * ..... xoxfo5ofxox&#xt ♦ 5 5 10 5 5 | 0 5 10 0 10 0 5 5 10 0 10 0 5 | 0 1 0 5 5 0 5 0 0 0 5 5 0 5 0 1 | * * * 2 * * * * * .xx.. .ox.. .....&#x ♦ 0 2 4 0 0 | 0 0 0 1 4 2 2 0 0 0 0 0 0 | 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 | * * * * 5 * * * * ..xxx ..xfo .....&#xt ♦ 0 0 4 4 2 | 0 0 0 0 0 2 2 0 4 2 4 1 0 | 0 0 0 0 0 0 0 1 0 2 2 0 2 0 0 0 | * * * * * 5 * * * ..xx. ..... ..xo.&#x ♦ 0 0 4 2 0 | 0 0 0 0 0 2 0 2 4 1 0 0 0 | 0 0 0 0 0 0 0 0 1 2 0 2 0 0 0 0 | * * * * * * 5 * * ...xx ..... ...ox&#x ♦ 0 0 0 2 4 | 0 0 0 0 0 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 | * * * * * * * 5 * ....x ....o5....x ♦ 0 0 0 0 10 | 0 0 0 0 0 0 0 0 0 0 0 5 10 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2 | * * * * * * * * 1
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