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Acronym
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daf, K-4.93
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Name
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decagonal antifastegium,
decagon - dap wedge,
{10} || gyro dip
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Segmentochoron display /
VRML
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⭳
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Circumradius
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sqrt[(258+61 sqrt(5)+sqrt[46850+20390 sqrt(5)])/241] = 1.702385
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Dihedral angles
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- at {3} between squippy and tet: arccos[-(3 sqrt(10+2 sqrt(5))-4)/8] = 157.908552°
- at {4} between dip and squippy: arccos[-sqrt((11+4 sqrt(5)-2 sqrt(50+22 sqrt(5)))/2)] = 96.430315°
- at {3} between dap and tet: arccos[-sqrt(-11+3 sqrt(5)+6 sqrt(5-2 sqrt(5)))/4] = 93.722962°
- at {3} between dap and squippy: arccos[sqrt(-11+3 sqrt(5)+6 sqrt(5-2 sqrt(5)))/4] = 86.277038°
- at {10} between dap and dap: arccos[(5-sqrt(5)-2 sqrt(5-2 sqrt(5)))/4] = 70.870054°
- at {10} between dap and dip: arccos[sqrt((-1+sqrt(5)+2 sqrt(5-2 sqrt(5)))/8)] = 54.564973°
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Face vector
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24, 64, 59, 19
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Confer
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- segmentochora family:
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n-af
n/d-af
- general polytopal classes:
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segmentochora
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External
links
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Incidence matrix according to Dynkin symbol
xoo10oxx&#x → height(1,2) = height(1,3) = sqrt[(1+2*cos(π/10))/(2+2*cos(π/10))] = 0.862397
height(2,3) = 1
({10} || (dual {10} || dual {10}))
o.. o.. | 10 * * | 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o. .o. | * 10 * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o ..o | * * 10 | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
------------+----------+-------------------+-------------------------+------------
x.. ... | 2 0 0 | 10 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.10oo.&#x | 1 1 0 | * 20 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o10o.o&#x | 1 0 1 | * * 20 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x. | 0 2 0 | * * * 10 * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo10.oo&#x | 0 1 1 | * * * * 10 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x | 0 0 2 | * * * * * 10 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
------------+----------+-------------------+-------------------------+------------
x..10o.. | 10 0 0 | 10 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 10 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 10 * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 10 * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 10 * * * * | 0 1 0 1 0
ooo10ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 20 * * * | 0 0 1 1 0
.o.10.x. | 0 10 0 | 0 0 0 10 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 10 * | 0 0 0 1 1
..o10..x | 0 0 10 | 0 0 0 0 0 10 | * * * * * * * * 1 | 0 1 0 0 1
------------+----------+-------------------+-------------------------+------------
xo.10ox.&#x ♦ 10 10 0 | 10 20 0 10 0 0 | 1 10 10 0 0 0 1 0 0 | 1 * * * *
x.o10o.x&#x ♦ 10 0 10 | 10 0 20 0 0 10 | 1 0 0 10 10 0 0 0 1 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 10 * *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * 10 *
.oo10.xx&#x ♦ 0 10 10 | 0 0 0 10 10 10 | 0 0 0 0 0 0 1 10 1 | * * * * 1
xo10ox ox&#x → height = sqrt[2 sqrt(50+22 sqrt(5))-4 sqrt(5)-9]/2 = 0.702658
({10} || gyro dip)
o. o. o. | 10 * | 2 4 0 0 | 1 4 2 2 0 0 | 2 2 1 0
.o .o .o | * 20 | 0 2 2 1 | 0 1 2 2 1 2 | 1 1 2 1
-------------+-------+-------------+-----------------+----------
x. .. .. | 2 0 | 10 * * * | 1 2 0 0 0 0 | 2 1 0 0
oo10oo oo&#x | 1 1 | * 40 * * | 0 1 1 1 0 0 | 1 1 1 0
.. .x .. | 0 2 | * * 20 * | 0 0 1 0 1 1 | 1 0 1 1
.. .. .x | 0 2 | * * * 10 | 0 0 0 2 0 2 | 0 1 2 1
-------------+-------+-------------+-----------------+----------
x.10o. .. | 10 0 | 10 0 0 0 | 1 * * * * * | 2 0 0 0
xo .. ..&#x | 2 1 | 1 2 0 0 | * 20 * * * * | 1 1 0 0
.. ox ..&#x | 1 2 | 0 2 1 0 | * * 20 * * * | 1 0 1 0
.. .. ox&#x | 1 2 | 0 2 0 1 | * * * 20 * * | 0 1 1 0
.o10.x .. | 0 10 | 0 0 10 0 | * * * * 2 * | 1 0 0 1
.. .x .x | 0 4 | 0 0 2 2 | * * * * * 10 | 0 0 1 1
-------------+-------+-------------+-----------------+----------
xo10ox ..&#x ♦ 10 10 | 10 20 10 0 | 1 10 10 0 1 0 | 2 * * *
xo .. ox&#x ♦ 2 2 | 1 4 0 1 | 0 2 0 2 0 0 | * 10 * *
.. ox ox&#x ♦ 1 4 | 0 4 2 2 | 0 0 2 2 0 1 | * * 10 *
.o10.x .x ♦ 0 20 | 0 0 20 10 | 0 0 0 0 2 10 | * * * 1
snubbed forms: xo10os2os
{10} || dap → height = sqrt[(9-sqrt(5)-2 sqrt(5-2 sqrt(5)))/8] = 0.814774
o.. o.. | 10 * * | 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o. .o. | * 10 * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o ..o | * * 10 | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
------------+----------+-------------------+-------------------------+------------
x.. ... | 2 0 0 | 10 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.10oo.&#x | 1 1 0 | * 20 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o10o.o&#x | 1 0 1 | * * 20 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x. | 0 2 0 | * * * 10 * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo10.oo&#x | 0 1 1 | * * * * 10 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x | 0 0 2 | * * * * * 10 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
------------+----------+-------------------+-------------------------+------------
x..10o.. | 10 0 0 | 10 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 10 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 10 * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 10 * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 10 * * * * | 0 1 0 1 0
ooo10ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 20 * * * | 0 0 1 1 0
.o.10.x. | 0 10 0 | 0 0 0 10 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 10 * | 0 0 0 1 1
..o10..x | 0 0 10 | 0 0 0 0 0 10 | * * * * * * * * 1 | 0 1 0 0 1
------------+----------+-------------------+-------------------------+------------
xo.10ox.&#x ♦ 10 10 0 | 10 20 0 10 0 0 | 1 10 10 0 0 0 1 0 0 | 1 * * * *
x.o10o.x&#x ♦ 10 0 10 | 10 0 20 0 0 10 | 1 0 0 10 10 0 0 0 1 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 10 * *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * 10 *
.oo10.xx&#x ♦ 0 10 10 | 0 0 0 10 10 10 | 0 0 0 0 0 0 1 10 1 | * * * * 1