CBSE Class 8 > Class 8 Videos > Regular and Irregular Polyhedron - Visualizing Shapes, Mathematics, CBSE Class 8
Regular and Irregular Polyhedron - Visualizing Shapes, CBSE Class 8 Video
FAQs on Regular and Irregular Polyhedron - Visualizing Shapes, Mathematics, CBSE Class 8
| 1. What is the difference between regular and irregular polyhedron? |  |
Ans. A regular polyhedron is a three-dimensional shape with congruent regular polygons as its faces, such as a cube or a tetrahedron. An irregular polyhedron, on the other hand, has faces that are not congruent regular polygons, meaning they have different side lengths or angles.
| 2. How can we visualize shapes of regular and irregular polyhedrons? | |
Ans. To visualize the shapes of regular polyhedrons, we can imagine them as having equal side lengths and angles. For example, a cube can be visualized as a six-sided figure with all sides and angles equal. Irregular polyhedrons, on the other hand, require a more flexible approach as their faces can have different side lengths and angles. We can use models, drawings, or computer simulations to help visualize irregular polyhedrons.
| 3. What are some examples of regular polyhedrons? | |
Ans. Some examples of regular polyhedrons include the tetrahedron (with four equilateral triangular faces), the cube (with six square faces), the octahedron (with eight equilateral triangular faces), the dodecahedron (with twelve regular pentagonal faces), and the icosahedron (with twenty equilateral triangular faces).
| 4. Can regular polyhedrons have curved faces? | |
Ans. No, regular polyhedrons cannot have curved faces. By definition, the faces of regular polyhedrons are congruent regular polygons, which means they have straight sides and angles. Curved faces would make a polyhedron irregular.
| 5. What are some practical applications of understanding regular and irregular polyhedrons? | |
Ans. Understanding regular and irregular polyhedrons is important in various fields such as architecture, engineering, and geometry. Architects use regular polyhedrons as the basis for designing buildings and structures. Engineers rely on the properties of regular polyhedrons to create stable and efficient designs. In geometry, regular polyhedrons are used to understand the properties of three-dimensional shapes and their relationship to other geometric concepts.
Text Transcript from Video
hello friends this video on visualizing
shapes part 8 is brought to you by exam
fear calm no more fear from exam now in
polyhedrons also we have different
categories like regular irregular
polyhedrons concave convex polyhedron so
let's start with regular polyhedrons the
word irregular what does it mean
regularity means equal so a polyhedron
is said to be regular if it's faces are
made up of regular polygons now do you
remember what a regular polygons these
are those polygons where all sides are
equal and all angles are equal for
example you can lateral triangle square
these are examples of regular polygons
so do you think that you can also have
polyhedrons which are made up of regular
polygons yes it is quite possible so if
you take the example of a cube so the
cube is made up of squares and squares
and regular polygons so cube is a
regular polyhedron but this is not the
only criteria for a polyhedron to be
regular this is just one criteria that
it should be made up of regular polygons
so this is our criterion number one what
does the criteria number two criteria
number two is that same number of faces
should meet at each vertex this is
criteria number two that means let's
think of this cube so think of any
vertex let's say I am assuming this
vertex so how many faces or how many
edges so if you look at this point how
many faces share this vertex so if you
see the top face the side face and the
front face
so three faces share this vertex so
every vertex should be shared by three
faces
so here you take this vertex so this
vertex is shared by the side face the
bottom face and the front face so in
this fashion the second criteria is that
in a regular polyhedron
each vertex should be shared by same
number of faces so let's take this
example what is this this is a
triangular pyramid so this is also a
pyramid but it is triangular pyramid
because the base is a triangle so let's
say this is the base and from the base
you have three trans this is one
triangle this is second triangle and the
backside one is the third triangle so
these three triangles they rise up and
meet at one point and that's how they
make a triangular pyramid so in this
triangular pyramid if you see each of
the phases so how many total phases are
there in this triangular pyramid there
are four phases and let's say that each
phase is an equilateral triangle so it's
assumed that each phase is equilateral
triangle so that means the phases are
made up of regular polygons so this
would this should be a a regular
polyhedron right but let's also look at
the second criteria second criteria see
is that at each vertex same number of
faces must meet so let's consider this
vertex so this vertex is shared by how
many faces the front this triangle right
so the backside triangle and the base
triangle so three faces meet at this
point similarly at this point all the
three triangles which is going on so all
the three triangles meet here so that
means in this case three triangles or
three pieces meet at each vertex so it
satisfies both the criteria and
therefore it is a regular polyhedra
let's look at the third example which is
a octahedron octahedron it's optimists
eight so this is a polyhedron with eight
faces so total this figure has eight
faces and what are each of those pieces
each face is a triangle so if you see
this is one face a triangle this is
another piece this one is yet another
face this is yet another face and
similarly you have for such triangular
face
the downward direction so you have a
total of eight triangular pieces and
each triangle is an equilateral triangle
which is a regular polygon therefore
this is a regular polyhedron what about
the second criteria so if you look at
any one X for example this vertex how
many triangles meet triangle number one
triangle number two triangle number
three and triangle number four so four
triangles meet at this vertex similarly
let's think of this point so here how
many triangles meet triangle number one
triangle number two triangle number
three and triangle number fourth so here
also four triangles meet at a point so
here we see that four phases meet at
each vertex so both the criteria are
satisfied and therefore this is also a
regular polyhedron so the name of this
regular polyhedron is octahedron that
means a polyhedron with eight faces and
what was this this was a triangular
pyramid now what about the eat regular
polyhedron so let's look at their
examples now when any of those those two
criteria is not met then the polyhedron
is an irregular polyhedron so here on
the screen we have some figures so let's
find out which one is is an irregular
polyhedron and why so let's start with a
cuboid so in case of a cuboid the first
criteria fails
why because it is not made up of regular
polygons rectangle is not a regular
polygon so rectangle is an irregular
polygon so therefore this quasi Hedren
is an irregular polyhedron so the first
criteria failure let's look at the
second example where we look at this
pyramid so this pyramid has a
quadrilateral base and three
triangles so any look at the
quadrilateral is not a regular polygon
so therefore in this case also the first
criteria fails because it is not made up
of regular polygons
third let's talk about the cylinder so
in case of a cylinder it is not even a
polyhedron because it is made up of
curved surface so this cylinder is Allah
is not a polyhedron or thought so since
it is not a polyhedron there is no point
talking about whether it is regular or
irregular fourth example let's think of
the hexahedron what is exciton examine
sticks so it is a polyhedron with six
faces so here each faces a triangular
face so it has six triangular faces so
in this case each of these triangle
might be an equilateral triangle so that
means the first criteria might get
satisfied but what about the second
criteria will that get satisfied so
let's analyze X is drawn in more detail
let's analyze why is this hexahedron an
irregular polygon select C so here on
the screen I have shown very distinctly
what are the six triangular faces of
this polyhedron so if you look in the
first diagram so this green triangle is
one phase this green triangle is the
second phase and this total great angle
which is on the back side is the third
phase similarly below this is the fourth
phase this is the fifth phase and this
entire thing towards the back is the
sixth phase so that's how there are six
phases in this triangle but still it is
not regular why is it not a regular
polyhedron that's because the second
criteria is not met so if you look at
the second criteria let's analyze
the total number of pieces that meet at
a point select smile to this point as a
and let's mark this vertex as B so let's
see that how many faces meet at vertex a
so at vertex a phases one two and three
so all of these meet at the vertex a so
that means a total of three faces made
at vertex a what happens at vertex B so
at vertex B the triangles one four
because four also means at point B and
six the six also meets at also meets at
point B so do you do can you think of
any other fees which means at point B
yes face number three also meets at
point B so basically vertex a at vertex
a the triangles 1 2 & 3 need whereas at
vertex B the triangles 1 4 6 & 3 so all
of these means so that means how many
faces need four faces meet at point B so
do we have the same number of pieces
meeting at each vertex no so that means
the second criteria has failed and
therefore this is an irregular
polyhedron so whenever you come across a
polyhedron there you are not very sure
if each face is a regular polygon or not
then you also need to make sure that the
second criteria is meeting or not so
meeting of so it is very important that
both the criteria is met for a
polyhedron to be a regular polyhedron
thank you please visit examview dot-com
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updates thank you
shapes part 8 is brought to you by exam
fear calm no more fear from exam now in
polyhedrons also we have different
categories like regular irregular
polyhedrons concave convex polyhedron so
let's start with regular polyhedrons the
word irregular what does it mean
regularity means equal so a polyhedron
is said to be regular if it's faces are
made up of regular polygons now do you
remember what a regular polygons these
are those polygons where all sides are
equal and all angles are equal for
example you can lateral triangle square
these are examples of regular polygons
so do you think that you can also have
polyhedrons which are made up of regular
polygons yes it is quite possible so if
you take the example of a cube so the
cube is made up of squares and squares
and regular polygons so cube is a
regular polyhedron but this is not the
only criteria for a polyhedron to be
regular this is just one criteria that
it should be made up of regular polygons
so this is our criterion number one what
does the criteria number two criteria
number two is that same number of faces
should meet at each vertex this is
criteria number two that means let's
think of this cube so think of any
vertex let's say I am assuming this
vertex so how many faces or how many
edges so if you look at this point how
many faces share this vertex so if you
see the top face the side face and the
front face
so three faces share this vertex so
every vertex should be shared by three
faces
so here you take this vertex so this
vertex is shared by the side face the
bottom face and the front face so in
this fashion the second criteria is that
in a regular polyhedron
each vertex should be shared by same
number of faces so let's take this
example what is this this is a
triangular pyramid so this is also a
pyramid but it is triangular pyramid
because the base is a triangle so let's
say this is the base and from the base
you have three trans this is one
triangle this is second triangle and the
backside one is the third triangle so
these three triangles they rise up and
meet at one point and that's how they
make a triangular pyramid so in this
triangular pyramid if you see each of
the phases so how many total phases are
there in this triangular pyramid there
are four phases and let's say that each
phase is an equilateral triangle so it's
assumed that each phase is equilateral
triangle so that means the phases are
made up of regular polygons so this
would this should be a a regular
polyhedron right but let's also look at
the second criteria second criteria see
is that at each vertex same number of
faces must meet so let's consider this
vertex so this vertex is shared by how
many faces the front this triangle right
so the backside triangle and the base
triangle so three faces meet at this
point similarly at this point all the
three triangles which is going on so all
the three triangles meet here so that
means in this case three triangles or
three pieces meet at each vertex so it
satisfies both the criteria and
therefore it is a regular polyhedra
let's look at the third example which is
a octahedron octahedron it's optimists
eight so this is a polyhedron with eight
faces so total this figure has eight
faces and what are each of those pieces
each face is a triangle so if you see
this is one face a triangle this is
another piece this one is yet another
face this is yet another face and
similarly you have for such triangular
face
the downward direction so you have a
total of eight triangular pieces and
each triangle is an equilateral triangle
which is a regular polygon therefore
this is a regular polyhedron what about
the second criteria so if you look at
any one X for example this vertex how
many triangles meet triangle number one
triangle number two triangle number
three and triangle number four so four
triangles meet at this vertex similarly
let's think of this point so here how
many triangles meet triangle number one
triangle number two triangle number
three and triangle number fourth so here
also four triangles meet at a point so
here we see that four phases meet at
each vertex so both the criteria are
satisfied and therefore this is also a
regular polyhedron so the name of this
regular polyhedron is octahedron that
means a polyhedron with eight faces and
what was this this was a triangular
pyramid now what about the eat regular
polyhedron so let's look at their
examples now when any of those those two
criteria is not met then the polyhedron
is an irregular polyhedron so here on
the screen we have some figures so let's
find out which one is is an irregular
polyhedron and why so let's start with a
cuboid so in case of a cuboid the first
criteria fails
why because it is not made up of regular
polygons rectangle is not a regular
polygon so rectangle is an irregular
polygon so therefore this quasi Hedren
is an irregular polyhedron so the first
criteria failure let's look at the
second example where we look at this
pyramid so this pyramid has a
quadrilateral base and three
triangles so any look at the
quadrilateral is not a regular polygon
so therefore in this case also the first
criteria fails because it is not made up
of regular polygons
third let's talk about the cylinder so
in case of a cylinder it is not even a
polyhedron because it is made up of
curved surface so this cylinder is Allah
is not a polyhedron or thought so since
it is not a polyhedron there is no point
talking about whether it is regular or
irregular fourth example let's think of
the hexahedron what is exciton examine
sticks so it is a polyhedron with six
faces so here each faces a triangular
face so it has six triangular faces so
in this case each of these triangle
might be an equilateral triangle so that
means the first criteria might get
satisfied but what about the second
criteria will that get satisfied so
let's analyze X is drawn in more detail
let's analyze why is this hexahedron an
irregular polygon select C so here on
the screen I have shown very distinctly
what are the six triangular faces of
this polyhedron so if you look in the
first diagram so this green triangle is
one phase this green triangle is the
second phase and this total great angle
which is on the back side is the third
phase similarly below this is the fourth
phase this is the fifth phase and this
entire thing towards the back is the
sixth phase so that's how there are six
phases in this triangle but still it is
not regular why is it not a regular
polyhedron that's because the second
criteria is not met so if you look at
the second criteria let's analyze
the total number of pieces that meet at
a point select smile to this point as a
and let's mark this vertex as B so let's
see that how many faces meet at vertex a
so at vertex a phases one two and three
so all of these meet at the vertex a so
that means a total of three faces made
at vertex a what happens at vertex B so
at vertex B the triangles one four
because four also means at point B and
six the six also meets at also meets at
point B so do you do can you think of
any other fees which means at point B
yes face number three also meets at
point B so basically vertex a at vertex
a the triangles 1 2 & 3 need whereas at
vertex B the triangles 1 4 6 & 3 so all
of these means so that means how many
faces need four faces meet at point B so
do we have the same number of pieces
meeting at each vertex no so that means
the second criteria has failed and
therefore this is an irregular
polyhedron so whenever you come across a
polyhedron there you are not very sure
if each face is a regular polygon or not
then you also need to make sure that the
second criteria is meeting or not so
meeting of so it is very important that
both the criteria is met for a
polyhedron to be a regular polyhedron
thank you please visit examview dot-com
for free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class 6 to 12
on physics chemistry mathematics and by
along with practical videos so please
subscribe to our channel for daily
updates thank you
About this Video
Apr 18, 2026 Last updated
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