Acronym | srip | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Name |
small rhombated pentachoron, cantellated pentachoron | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Cross sections |
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Circumradius | sqrt(7/5) = 1.183216 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. oct | 3/sqrt(10) = 0.948683 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. trip | 7/sqrt(60) = 0.903696 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. co | sqrt(2/5) = 0.632456 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Vertex figure |
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Vertex layers |
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Lace city in approx. ASCII-art |
x3o o3x -- o3x3o (oct) x3o u3o x3x -- x3x3o (tut) o3x x3x x3o -- x3o3x (co) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
o o x x o o -- o3x3o (oct) o x x u u x x o -- x3x3o (tut) x x ou uo x x -- x3o3x (co) \ \ \ \ \ \ \ +-- o x3o ({3}) \ \ +------- x x3x (hip) \ +------------ ou uo3ox&#zx +----------------- x x3o (trip) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Volume | 73 sqrt(5)/48 = 3.400687 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Surface | [20 sqrt(2)+5 sqrt(3)]/2 = 18.472263 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
General of army | (is itself convex) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– other uniform polychoral members:
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Dihedral angles | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Dual | m3o3m3o | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 30, 90, 80, 20 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
Note that srip can be thought of as the external blend of 1 pen + 5 raps + 10 trafs + 10 pens + 5 copies. This decomposition is described as the (also subdimensioanlly) degenerate segmentoteron xo3ox3oo3ox&#x.
Incidence matrix according to Dynkin symbol
x3o3x3o . . . . | 30 ♦ 2 4 | 1 4 2 2 | 2 2 1 --------+----+-------+-------------+------- x . . . | 2 | 30 * | 1 2 0 0 | 2 1 0 . . x . | 2 | * 60 | 0 1 1 1 | 1 1 1 --------+----+-------+-------------+------- x3o . . | 3 | 3 0 | 10 * * * | 2 0 0 x . x . | 4 | 2 2 | * 30 * * | 1 1 0 . o3x . | 3 | 0 3 | * * 20 * | 1 0 1 . . x3o | 3 | 0 3 | * * * 20 | 0 1 1 --------+----+-------+-------------+------- x3o3x . ♦ 12 | 12 12 | 4 6 4 0 | 5 * * x . x3o ♦ 6 | 3 6 | 0 3 0 2 | * 10 * . o3x3o ♦ 6 | 0 12 | 0 0 4 4 | * * 5 snubbed forms: β3o3x3o, x3o3β3o, β3o3β3o
x3o3x3/2o . . . . | 30 ♦ 2 4 | 1 4 2 2 | 2 2 1 ----------+----+-------+-------------+------- x . . . | 2 | 30 * | 1 2 0 0 | 2 1 0 . . x . | 2 | * 60 | 0 1 1 1 | 1 1 1 ----------+----+-------+-------------+------- x3o . . | 3 | 3 0 | 10 * * * | 2 0 0 x . x . | 4 | 2 2 | * 30 * * | 1 1 0 . o3x . | 3 | 0 3 | * * 20 * | 1 0 1 . . x3/2o | 3 | 0 3 | * * * 20 | 0 1 1 ----------+----+-------+-------------+------- x3o3x . ♦ 12 | 12 12 | 4 6 4 0 | 5 * * x . x3/2o ♦ 6 | 3 6 | 0 3 0 2 | * 10 * . o3x3/2o ♦ 6 | 0 12 | 0 0 4 4 | * * 5
x3/2o3/2x3o . . . . | 30 ♦ 2 4 | 1 4 2 2 | 2 2 1 ------------+----+-------+-------------+------- x . . . | 2 | 30 * | 1 2 0 0 | 2 1 0 . . x . | 2 | * 60 | 0 1 1 1 | 1 1 1 ------------+----+-------+-------------+------- x3/2o . . | 3 | 3 0 | 10 * * * | 2 0 0 x . x . | 4 | 2 2 | * 30 * * | 1 1 0 . o3/2x . | 3 | 0 3 | * * 20 * | 1 0 1 . . x3o | 3 | 0 3 | * * * 20 | 0 1 1 ------------+----+-------+-------------+------- x3/2o3/2x . ♦ 12 | 12 12 | 4 6 4 0 | 5 * * x . x3o ♦ 6 | 3 6 | 0 3 0 2 | * 10 * . o3/2x3o ♦ 6 | 0 12 | 0 0 4 4 | * * 5
x3/2o3/2x3/2o . . . . | 30 ♦ 2 4 | 1 4 2 2 | 2 2 1 --------------+----+-------+-------------+------- x . . . | 2 | 30 * | 1 2 0 0 | 2 1 0 . . x . | 2 | * 60 | 0 1 1 1 | 1 1 1 --------------+----+-------+-------------+------- x3/2o . . | 3 | 3 0 | 10 * * * | 2 0 0 x . x . | 4 | 2 2 | * 30 * * | 1 1 0 . o3/2x . | 3 | 0 3 | * * 20 * | 1 0 1 . . x3/2o | 3 | 0 3 | * * * 20 | 0 1 1 --------------+----+-------+-------------+------- x3/2o3/2x . ♦ 12 | 12 12 | 4 6 4 0 | 5 * * x . x3/2o ♦ 6 | 3 6 | 0 3 0 2 | * 10 * . o3/2x3/2o ♦ 6 | 0 12 | 0 0 4 4 | * * 5
oxx3xxo3oox&#xt → both heights = sqrt(5/8) = 0.790569 (oct || pseudo tut || co) o..3o..3o.. | 6 * * ♦ 4 2 0 0 0 0 0 | 2 2 1 4 0 0 0 0 0 0 0 | 1 2 2 0 0 0 .o.3.o.3.o. | * 12 * ♦ 0 1 1 2 2 0 0 | 0 0 1 2 1 2 2 1 0 0 0 | 0 2 1 1 1 0 ..o3..o3..o | * * 12 ♦ 0 0 0 0 2 2 2 | 0 0 0 0 0 2 1 2 1 2 1 | 0 1 0 2 1 1 ----------------+---------+---------------------+---------------------------+------------ ... x.. ... | 2 0 0 | 12 * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0 oo.3oo.3oo.&#x | 1 1 0 | * 12 * * * * * | 0 0 1 2 0 0 0 0 0 0 0 | 0 2 1 0 0 0 .x. ... ... | 0 2 0 | * * 6 * * * * | 0 0 1 0 0 2 0 0 0 0 0 | 0 2 0 1 0 0 ... .x. ... | 0 2 0 | * * * 12 * * * | 0 0 0 1 1 0 1 0 0 0 0 | 0 1 1 0 1 0 .oo3.oo3.oo&#x | 0 1 1 | * * * * 24 * * | 0 0 0 0 0 1 1 1 0 0 0 | 0 1 0 1 1 0 ..x ... ... | 0 0 2 | * * * * * 12 * | 0 0 0 0 0 1 0 0 1 1 0 | 0 1 0 1 0 1 ... ... ..x | 0 0 2 | * * * * * * 12 | 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1 ----------------+---------+---------------------+---------------------------+------------ o..3x.. ... | 3 0 0 | 3 0 0 0 0 0 0 | 4 * * * * * * * * * * | 1 1 0 0 0 0 ... x..3o.. | 3 0 0 | 3 0 0 0 0 0 0 | * 4 * * * * * * * * * | 1 0 1 0 0 0 ox. ... ...&#x | 1 2 0 | 0 2 1 0 0 0 0 | * * 6 * * * * * * * * | 0 2 0 0 0 0 ... xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0 0 ... .x.3.o. | 0 3 0 | 0 0 0 3 0 0 0 | * * * * 4 * * * * * * | 0 0 1 0 1 0 .xx ... ...&#x | 0 2 2 | 0 0 1 0 2 1 0 | * * * * * 12 * * * * * | 0 1 0 1 0 0 ... .xo ...&#x | 0 2 1 | 0 0 0 1 2 0 0 | * * * * * * 12 * * * * | 0 1 0 0 1 0 ... ... .ox&#x | 0 1 2 | 0 0 0 0 2 0 1 | * * * * * * * 12 * * * | 0 0 0 1 1 0 ..x3..o ... | 0 0 3 | 0 0 0 0 0 3 0 | * * * * * * * * 4 * * | 0 1 0 0 0 1 ..x ... ..x | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * * * * 6 * | 0 0 0 1 0 1 ... ..o3..x | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * * 4 | 0 0 0 0 1 1 ----------------+---------+---------------------+---------------------------+------------ o..3x..3o.. ♦ 6 0 0 | 12 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 | 1 * * * * * oxx3xxo ...&#xt ♦ 3 6 3 | 3 6 3 3 6 3 0 | 1 0 3 3 0 3 3 0 1 0 0 | * 4 * * * * ... xx.3oo.&#x ♦ 3 3 0 | 3 3 0 3 0 0 0 | 0 1 0 3 1 0 0 0 0 0 0 | * * 4 * * * .xx ... .ox&#x ♦ 0 2 4 | 0 0 1 0 4 2 2 | 0 0 0 0 0 2 0 2 0 1 0 | * * * 6 * * ... .xo3.ox&#x ♦ 0 3 3 | 0 0 0 3 6 0 3 | 0 0 0 0 1 0 3 3 0 0 1 | * * * * 4 * ..x3..o3..x ♦ 0 0 12 | 0 0 0 0 0 12 12 | 0 0 0 0 0 0 0 0 4 6 4 | * * * * * 1
x(uo)xo x(ou)xx3o(xo)xo&#xt all 3 heights = sqrt(5/12) = 0.645497 (trip || compound of gyrated pseudo u x3o and (ungyrated) u-{3} || pseudo hip || {3}) o(..).. o(..)..3o(..).. | 6 * * * * ♦ 1 2 2 1 0 0 0 0 0 0 0 0 | 2 1 2 1 1 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0 .(o.).. .(o.)..3.(o.).. | * 6 * * * ♦ 0 0 2 0 2 2 0 0 0 0 0 0 | 0 0 1 2 0 2 1 1 2 0 0 0 0 0 0 0 | 0 1 1 2 1 0 0 .(.o).. .(.o)..3.(.o).. | * * 3 * * ♦ 0 0 0 2 0 0 4 0 0 0 0 0 | 0 0 0 0 1 4 0 0 0 2 2 0 0 0 0 0 | 0 0 2 2 0 1 0 .(..)o. .(..)o.3.(..)o. | * * * 12 * ♦ 0 0 0 0 0 1 1 1 1 1 1 0 | 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 | 0 0 1 1 1 1 1 .(..).o .(..).o3.(..).o | * * * * 3 ♦ 0 0 0 0 0 0 0 0 0 0 4 2 | 0 0 0 0 0 0 0 0 0 0 0 0 2 4 2 1 | 0 0 0 0 2 1 2 ----------------------------+------------+-----------------------------+----------------------------------+-------------- x(..).. .(..).. .(..).. | 2 0 0 0 0 | 3 * * * * * * * * * * * | 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 0 2 0 0 0 0 .(..).. x(..).. .(..).. | 2 0 0 0 0 | * 6 * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 o(o.).. o(o.)..3o(o.)..&#x | 1 1 0 0 0 | * * 12 * * * * * * * * * | 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 o(.o).. o(.o)..3o(.o)..&#x | 1 0 1 0 0 | * * * 6 * * * * * * * * | 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 | 0 0 2 1 0 0 0 .(..).. .(..).. .(x.).. | 0 2 0 0 0 | * * * * 6 * * * * * * * | 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 | 0 1 0 1 1 0 0 .(o.)o. .(o.)o.3.(o.)o.&#x | 0 1 0 1 0 | * * * * * 12 * * * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 .(.o)o. .(.o)o.3.(.o)o.&#x | 0 0 1 1 0 | * * * * * * 12 * * * * * | 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 | 0 0 1 1 0 1 0 .(..)x. .(..).. .(..).. | 0 0 0 2 0 | * * * * * * * 6 * * * * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 | 0 0 1 0 0 1 1 .(..).. .(..)x. .(..).. | 0 0 0 2 0 | * * * * * * * * 6 * * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 | 0 0 1 0 1 0 1 .(..).. .(..).. .(..)x. | 0 0 0 2 0 | * * * * * * * * * 6 * * | 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 | 0 0 0 1 1 1 0 .(..)oo .(..)oo3.(..)oo&#x | 0 0 0 1 1 | * * * * * * * * * * 12 * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 | 0 0 0 0 1 1 1 .(..).. .(..).x .(..).. | 0 0 0 0 2 | * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 | 0 0 0 0 2 0 1 ----------------------------+------------+-----------------------------+----------------------------------+-------------- x(..).. x(..).. .(..).. | 4 0 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 .(..).. x(..)..3o(..).. | 3 0 0 0 0 | 0 3 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 .(..).. x(o.).. .(..)..&#x | 2 1 0 0 0 | 0 1 2 0 0 0 0 0 0 0 0 0 | * * 6 * * * * * * * * * * * * * | 0 1 1 0 0 0 0 .(..).. .(..).. o(x.)..&#x | 1 2 0 0 0 | 0 0 2 0 1 0 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * * | 0 1 0 1 0 0 0 x(.o).. .(..).. .(..)..&#x | 2 0 1 0 0 | 1 0 0 2 0 0 0 0 0 0 0 0 | * * * * 3 * * * * * * * * * * * | 0 0 2 0 0 0 0 o(oo)o. o(oo)o.3o(oo)o.&#xr | 1 1 1 1 0 | 0 0 1 1 0 1 1 0 0 0 0 0 | * * * * * 12 * * * * * * * * * * | 0 0 1 1 0 0 0 .(..).. .(o.)..3.(x.).. | 0 3 0 0 0 | 0 0 0 0 3 0 0 0 0 0 0 0 | * * * * * * 2 * * * * * * * * * | 0 1 0 0 1 0 0 .(..).. .(o.)x. .(..)..&#x | 0 1 0 2 0 | 0 0 0 0 0 2 0 0 1 0 0 0 | * * * * * * * 6 * * * * * * * * | 0 0 1 0 1 0 0 .(..).. .(..).. .(x.)x.&#x | 0 2 0 2 0 | 0 0 0 0 1 2 0 0 0 1 0 0 | * * * * * * * * 6 * * * * * * * | 0 0 0 1 1 0 0 .(.o)x. .(..).. .(..)..&#x | 0 0 1 2 0 | 0 0 0 0 0 0 2 1 0 0 0 0 | * * * * * * * * * 6 * * * * * * | 0 0 1 0 0 1 0 .(..).. .(..).. .(.o)x.&#x | 0 0 1 2 0 | 0 0 0 0 0 0 2 0 0 1 0 0 | * * * * * * * * * * 6 * * * * * | 0 0 0 1 0 1 0 .(..)x. .(..)x. .(..).. | 0 0 0 4 0 | 0 0 0 0 0 0 0 2 2 0 0 0 | * * * * * * * * * * * 3 * * * * | 0 0 1 0 0 0 1 .(..)xo .(..).. .(..)..&#x | 0 0 0 2 1 | 0 0 0 0 0 0 0 1 0 0 2 0 | * * * * * * * * * * * * 6 * * * | 0 0 0 0 0 1 1 .(..).. .(..)xx .(..)..&#x | 0 0 0 2 2 | 0 0 0 0 0 0 0 0 1 0 2 1 | * * * * * * * * * * * * * 6 * * | 0 0 0 0 1 0 1 .(..).. .(..).. .(..)xo&#x | 0 0 0 2 1 | 0 0 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * * 6 * | 0 0 0 0 1 1 0 .(..).. .(..).x3.(..).o | 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * 1 | 0 0 0 0 2 0 0 ----------------------------+------------+-----------------------------+----------------------------------+-------------- x(..).. x(..)..3o(..).. ♦ 6 0 0 0 0 | 3 6 0 0 0 0 0 0 0 0 0 0 | 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * .(..).. x(o.)..3o(x.)..&#x ♦ 3 3 0 0 0 | 0 3 6 0 3 0 0 0 0 0 0 0 | 0 1 3 3 0 0 1 0 0 0 0 0 0 0 0 0 | * 2 * * * * * x(uo)x. x(ou)x. .(..)..&#xt ♦ 4 2 2 4 0 | 2 2 4 4 0 4 4 2 2 0 0 0 | 1 0 2 0 2 4 0 2 0 2 0 1 0 0 0 0 | * * 3 * * * * .(..).. .(..).. o(xo)x.&#xr ♦ 1 2 1 2 0 | 0 0 2 1 1 2 2 0 0 1 0 0 | 0 0 0 1 0 2 0 0 1 0 1 0 0 0 0 0 | * * * 6 * * * .(..).. .(o.)xx3.(x.)xo&#xt ♦ 0 3 0 6 3 | 0 0 0 0 3 6 0 0 3 3 6 3 | 0 0 0 0 0 0 1 3 3 0 0 0 0 3 3 1 | * * * * 2 * * .(.o)xo .(..).. .(.o)xo&#xt ♦ 0 0 1 4 1 | 0 0 0 0 0 0 4 2 0 2 4 0 | 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 0 | * * * * * 3 * .(..)xo .(..)xx .(..)..&#x ♦ 0 0 0 4 2 | 0 0 0 0 0 0 0 2 2 0 4 1 | 0 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 | * * * * * * 3
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