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schema-hoomd.rst

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HOOMD Schema

HOOMD-blue supports a wide variety of per particle attributes and properties. Particles, bonds, and types can be dynamically added and removed during simulation runs. The hoomd schema can handle all of these situations in a reasonably space efficient and high performance manner. It is also backwards compatible with previous versions of itself, as we only add new additional data chunks in new versions and do not change the interpretation of the existing data chunks. Any newer reader will initialize new data chunks with default values when they are not present in an older version file.

Schema name:hoomd
Schema version:1.4
.. seealso::

    `hoomd.State` for a full description of how HOOMD interprets this
    data.

Use-cases

The GSD schema hoomd provides:

  1. Every frame of GSD output is viable to restart a simulation
  2. Support varying numbers of particles, bonds, etc...
  3. Support varying attributes (type, mass, etc...)
  4. Support orientation, angular momentum, and other fields.
  5. Binary format on disk
  6. High performance file read and write
  7. Support logging computed quantities

Data chunks

Each frame the hoomd schema may contain one or more data chunks. The layout and names of the chunksmatch that of the binary snapshot API in HOOMD-blue itself. Data chunks are organized in categories. These categories have no meaning in the hoomd schema specification, and are simply an organizational tool. Some file writers may implement options that act on categories (i.e. write attributes out to every frame, or just frame 0).

Values are well defined for all fields at all frames. When a data chunk is present in frame i, it defines the values for the frame. When it is not present, the data chunk of the same name at frame 0 defines the values for frame i (when N is equal between the frames). If the data chunk is not present in frame 0, or N differs between frames, values are default. Default values allow files sizes to remain small. For example, a simulation with point particles where orientation is always (1,0,0,0) would not write any orientation chunk to the file.

N may be zero. When N is zero, an index entry may be written for a data chunk with no actual data written to the file for that chunk.

Name Category Type Size Default Units
Configuration          
:chunk:`configuration/step`   uint64 1x1 0 number
:chunk:`configuration/dimensions`   uint8 1x1 3 number
:chunk:`configuration/box`   float 6x1   varies
Particle data          
:chunk:`particles/N` attribute uint32 1x1 0 number
:chunk:`particles/types` attribute int8 NTxM ['A'] UTF-8
:chunk:`particles/typeid` attribute uint32 Nx1 0 number
:chunk:`particles/type_shapes` attribute int8 NTxM   UTF-8
:chunk:`particles/mass` attribute float Nx1 1.0 mass
:chunk:`particles/charge` attribute float Nx1 0.0 charge
:chunk:`particles/diameter` attribute float Nx1 1.0 length
:chunk:`particles/body` attribute int32 Nx1 -1 number
:chunk:`particles/moment_inertia` attribute float Nx3 0,0,0 mass * length^2
:chunk:`particles/position` property float Nx3 0,0,0 length
:chunk:`particles/orientation` property float Nx4 1,0,0,0 unit quaternion
:chunk:`particles/velocity` momentum float Nx3 0,0,0 length/time
:chunk:`particles/angmom` momentum float Nx4 0,0,0,0 quaternion
:chunk:`particles/image` momentum int32 Nx3 0,0,0 number
Bond data          
:chunk:`bonds/N` topology uint32 1x1 0 number
:chunk:`bonds/types` topology int8 NTxM   UTF-8
:chunk:`bonds/typeid` topology uint32 Nx1 0 number
:chunk:`bonds/group` topology uint32 Nx2 0,0 number
Angle data          
:chunk:`angles/N` topology uint32 1x1 0 number
:chunk:`angles/types` topology int8 NTxM   UTF-8
:chunk:`angles/typeid` topology uint32 Nx1 0 number
:chunk:`angles/group` topology uint32 Nx3 0,0,0 number
Dihedral data          
:chunk:`dihedrals/N` topology uint32 1x1 0 number
:chunk:`dihedrals/types` topology int8 NTxM   UTF-8
:chunk:`dihedrals/typeid` topology uint32 Nx1 0 number
:chunk:`dihedrals/group` topology uint32 Nx4 0,0,0,0 number
Improper data          
:chunk:`impropers/N` topology uint32 1x1 0 number
:chunk:`impropers/types` topology int8 NTxM   UTF-8
:chunk:`impropers/typeid` topology uint32 Nx1 0 number
:chunk:`impropers/group` topology uint32 Nx4 0,0,0,0 number
Constraint data          
:chunk:`constraints/N` topology uint32 1x1 0 number
:chunk:`constraints/value` topology float Nx1 0 length
:chunk:`constraints/group` topology uint32 Nx2 0,0 number
Special pairs data          
:chunk:`pairs/N` topology uint32 1x1 0 number
:chunk:`pairs/types` topology int8 NTxM   utf-8
:chunk:`pairs/typeid` topology uint32 Nx1 0 number
:chunk:`pairs/group` topology uint32 Nx2 0,0 number

Configuration

.. chunk:: configuration/step

    :Type: uint64
    :Size: 1x1
    :Default: 0
    :Units: number

    Simulation time step.

.. chunk:: configuration/dimensions

    :Type: uint8
    :Size: 1x1
    :Default: 3
    :Units: number

    Number of dimensions in the simulation. Must be 2 or 3.

    .. note::
        When using `gsd.hoomd.Snapshot`, the object will try to intelligently default to a
        dimension. When setting a box with :math:`L_z = 0`, ``dimensions`` will default to
        2 otherwise 3. Explicit setting of this value by users always takes precedence.

.. chunk:: configuration/box

    :Type: float
    :Size: 6x1
    :Default: [1,1,1,0,0,0]
    :Units: *varies*

    Simulation box. Each array element defines a different box property. See the
    hoomd documentation for a full description on how these box parameters map
    to a triclinic geometry.

    * ``box[0:3]``: :math:`(l_x, l_y, l_z)` the box length in each direction, in length units
    * ``box[3:]``: :math:`(xy, xz, yz)` the tilt factors, dimensionless values


Particle data

Within a single frame, the number of particles N and NT are fixed for all chunks. N and NT may vary from one frame to the next. All values are stored in hoomd native units.

Attributes

.. chunk:: particles/N

    :Type: uint32
    :Size: 1x1
    :Default: 0
    :Units: number

    Define *N*, the number of particles, for all data chunks ``particles/*``.

.. chunk:: particles/types

    :Type: int8
    :Size: NTxM
    :Default: ['A']
    :Units: UTF-8

    Implicitly define *NT*, the number of particle types, for all data chunks
    ``particles/*``. *M* must be large enough to accommodate each type name as a
    null terminated UTF-8 character string. Row *i* of the 2D matrix is the type
    name for particle type *i*.

.. chunk:: particles/typeid

    :Type: uint32
    :Size: Nx1
    :Default: 0
    :Units: number

    Store the type id of each particle. All id's must be less than *NT*. A
    particle with type *id* has a type name matching the corresponding row in
    :chunk:`particles/types`.

.. chunk:: particles/type_shapes

    :Type: int8
    :Size: NTxM
    :Default: *empty*
    :Units: UTF-8

    Store a per-type shape definition for visualization. A dictionary is stored
    for each of the *NT* types, corresponding to a shape for visualization of
    that type. *M* must be large enough to accommodate the shape definition as
    a null-terminated UTF-8 JSON-encoded string. See: :ref:`shapes` for
    examples.

.. chunk:: particles/mass

    :Type: float (32-bit)
    :Size: Nx1
    :Default: 1.0
    :Units: mass

    Store the mass of each particle.

.. chunk:: particles/charge

    :Type: float (32-bit)
    :Size: Nx1
    :Default: 0.0
    :Units: charge

    Store the charge of each particle.

.. chunk:: particles/diameter

    :Type: float (32-bit)
    :Size: Nx1
    :Default: 1.0
    :Units: length

    Store the diameter of each particle.

.. chunk:: particles/body

    :Type: int32
    :Size: Nx1
    :Default: -1
    :Units: number

    Store the composite body associated with each particle. The value -1
    indicates no body. The body field may be left out of input files, as hoomd
    will create the needed constituent particles.

.. chunk:: particles/moment_inertia

    :Type: float (32-bit)
    :Size: Nx3
    :Default: 0,0,0
    :Units: mass * length^2

    Store the moment_inertia of each particle :math:`(I_{xx}, I_{yy}, I_{zz})`.
    This inertia tensor is diagonal in the body frame of the particle. The
    default value is for point particles.

Properties

.. chunk:: particles/position

    :Type: float (32-bit)
    :Size: Nx3
    :Default: 0,0,0
    :Units: length

    Store the position of each particle (*x*, *y*, *z*).

    All particles in the simulation are referenced by a tag. The position data
    chunk (and all other per particle data chunks) list particles in tag order.
    The first particle listed has tag 0, the second has tag 1, ..., and the last
    has tag N-1 where N is the number of particles in the simulation.

    All particles must be inside the box:

    * :math:`-l_x/2 + (xz-xy \cdot yz) \cdot z + xy \cdot y \le x < l_x/2 + (xz-xy \cdot yz) \cdot z + xy \cdot  y`
    * :math:`-l_y/2 + yz \cdot z \le y < l_y/2 + yz \cdot z`
    * :math:`-l_z/2 \le z < l_z/2`

    Where :math:`l_x`, :math:`l_y`, :math:`l_z`, :math:`xy`, :math:`xz`, and :math:`yz` are the
    simulation box parameters (:chunk:`configuration/box`).

.. chunk:: particles/orientation

    :Type: float (32-bit)
    :Size: Nx4
    :Default: 1,0,0,0
    :Units: unit quaternion

    Store the orientation of each particle. In scalar + vector notation, this is
    :math:`(r, a_x, a_y, a_z)`,
    where the quaternion is :math:`q = r + a_xi + a_yj + a_zk`. A unit
    quaternion has the property: :math:`\sqrt{r^2 + a_x^2 + a_y^2 + a_z^2} = 1`.

Momenta

.. chunk:: particles/velocity

    :Type: float (32-bit)
    :Size: Nx3
    :Default: 0,0,0
    :Units: length/time

    Store the velocity of each particle :math:`(v_x, v_y, v_z)`.

.. chunk:: particles/angmom

    :Type: float (32-bit)
    :Size: Nx4
    :Default: 0,0,0,0
    :Units: quaternion

    Store the angular momentum of each particle as a quaternion. See the HOOMD
    documentation for information on how to convert to a vector representation.

.. chunk:: particles/image

    :Type: int32
    :Size: Nx3
    :Default: 0,0,0
    :Units: number

    Store the number of times each particle has wrapped around the box
    :math:`(i_x, i_y, i_z)`. In constant volume simulations, the unwrapped
    position in the particle's full trajectory is

    * :math:`x_u = x + i_x \cdot l_x + xy \cdot i_y \cdot l_y + xz \cdot i_z \cdot l_z`
    * :math:`y_u = y + i_y \cdot l_y + yz \cdot i_z \cdot l_z`
    * :math:`z_u = z + i_z \cdot l_z`

Topology

.. chunk:: bonds/N

    :Type: uint32
    :Size: 1x1
    :Default: 0
    :Units: number

    Define *N*, the number of bonds, for all data chunks ``bonds/*``.

.. chunk:: bonds/types

    :Type: int8
    :Size: NTxM
    :Default: *empty*
    :Units: UTF-8

    Implicitly define *NT*, the number of bond types, for all data chunks
    ``bonds/*``. *M* must be large enough to accommodate each type name as a
    null terminated UTF-8 character string. Row *i* of the 2D matrix is the type
    name for bond type *i*. By default, there are 0 bond types.

.. chunk:: bonds/typeid

    :Type: uint32
    :Size: Nx1
    :Default: 0
    :Units: number

    Store the type id of each bond. All id's must be less than *NT*. A bond with
    type *id* has a type name matching the corresponding row in
    :chunk:`bonds/types`.

.. chunk:: bonds/group

    :Type: uint32
    :Size: Nx2
    :Default: 0,0
    :Units: number

    Store the particle tags in each bond.

.. chunk:: angles/N

    :Type: uint32
    :Size: 1x1
    :Default: 0
    :Units: number

    Define *N*, the number of angles, for all data chunks ``angles/*``.

.. chunk:: angles/types

    :Type: int8
    :Size: NTxM
    :Default: *empty*
    :Units: UTF-8

    Implicitly define *NT*, the number of angle types, for all data chunks
    ``angles/*``. *M* must be large enough to accommodate each type name as a
    null terminated UTF-8 character string. Row *i* of the 2D matrix is the type
    name for angle type *i*. By default, there are 0 angle types.

.. chunk:: angles/typeid

    :Type: uint32
    :Size: Nx1
    :Default: 0
    :Units: number

    Store the type id of each angle. All id's must be less than *NT*. A angle
    with type *id* has a type name matching the corresponding row in
    :chunk:`angles/types`.

.. chunk:: angles/group

    :Type: uint32
    :Size: Nx3
    :Default: 0,0,0
    :Units: number

    Store the particle tags in each angle.

.. chunk:: dihedrals/N

    :Type: uint32
    :Size: 1x1
    :Default: 0
    :Units: number

    Define *N*, the number of dihedrals, for all data chunks ``dihedrals/*``.

.. chunk:: dihedrals/types

    :Type: int8
    :Size: NTxM
    :Default: *empty*
    :Units: UTF-8

    Implicitly define *NT*, the number of dihedral types, for all data chunks
    ``dihedrals/*``. *M* must be large enough to accommodate each type name as a
    null terminated UTF-8 character string. Row *i* of the 2D matrix is the type
    name for dihedral type *i*. By default, there are 0 dihedral types.

.. chunk:: dihedrals/typeid

    :Type: uint32
    :Size: Nx1
    :Default: 0
    :Units: number

    Store the type id of each dihedral. All id's must be less than *NT*. A
    dihedral with type *id* has a type name matching the corresponding row in
    :chunk:`dihedrals/types`.

.. chunk:: dihedrals/group

    :Type: uint32
    :Size: Nx4
    :Default: 0,0,0,0
    :Units: number

    Store the particle tags in each dihedral.

.. chunk:: impropers/N

    :Type: uint32
    :Size: 1x1
    :Default: 0
    :Units: number

    Define *N*, the number of impropers, for all data chunks ``impropers/*``.

.. chunk:: impropers/types

    :Type: int8
    :Size: NTxM
    :Default: *empty*
    :Units: UTF-8

    Implicitly define *NT*, the number of improper types, for all data chunks
    ``impropers/*``. *M* must be large enough to accommodate each type name as a
    null terminated UTF-8 character string. Row *i* of the 2D matrix is the type
    name for improper type *i*. By default, there are 0 improper types.

.. chunk:: impropers/typeid

    :Type: uint32
    :Size: Nx1
    :Default: 0
    :Units: number

    Store the type id of each improper. All id's must be less than *NT*. A
    improper with type *id* has a type name matching the corresponding row in
    :chunk:`impropers/types`.

.. chunk:: impropers/group

    :Type: uint32
    :Size: Nx4
    :Default: 0,0,0,0
    :Units: number

    Store the particle tags in each improper.

.. chunk:: constraints/N

    :Type: uint32
    :Size: 1x1
    :Default: 0
    :Units: number

    Define *N*, the number of constraints, for all data chunks
    ``constraints/*``.

.. chunk:: constraints/value

    :Type: float
    :Size: Nx1
    :Default: 0
    :Units: length

    Store the distance of each constraint. Each constraint defines a fixed
    distance between two particles.

.. chunk:: constraints/group

    :Type: uint32
    :Size: Nx2
    :Default: 0,0
    :Units: number

    Store the particle tags in each constraint.

.. chunk:: pairs/N

    :Type: uint32
    :Size: 1x1
    :Default: 0
    :Units: number

    Define *N*, the number of special pair interactions, for all data chunks
    ``pairs/*``.

    .. versionadded:: 1.1

.. chunk:: pairs/types

    :Type: int8
    :Size: NTxM
    :Default: *empty*
    :Units: UTF-8

    Implicitly define *NT*, the number of special pair types, for all data
    chunks ``pairs/*``. *M* must be large enough to accommodate each type name
    as a null terminated UTF-8 character string. Row *i* of the 2D matrix is the
    type name for particle type *i*. By default, there are 0 special pair types.

    .. versionadded:: 1.1

.. chunk:: pairs/typeid

    :Type: uint32
    :Size: Nx1
    :Default: 0
    :Units: number

    Store the type id of each special pair interaction. All id's must be less
    than *NT*. A pair with type *id* has a type name matching the corresponding
    row in :chunk:`pairs/types`.

    .. versionadded:: 1.1

.. chunk:: pairs/group

    :Type: uint32
    :Size: Nx2
    :Default: 0,0
    :Units: number

    Store the particle tags in each special pair interaction.

    .. versionadded:: 1.1

Logged data

Users may store logged data in log/* data chunks. Logged data encompasses values computed at simulation time that are too expensive or cumbersome to re-compute in post processing. This specification does not define specific chunk names or define logged data. Users may select any valid name for logged data chunks as appropriate for their workflow.

For any named logged data chunks present in any frame frame the file: If a chunk is not present in a given frame i != 0, the implementation should provide the quantity as read from frame 0 for that frame. GSD files that include a logged data chunk only in some frames i != 0 and not in frame 0 are invalid.

By convention, per-particle and per-bond logged data should have a chunk name starting with log/particles/ and log/bonds, respectively. Scalar, vector, and string values may be stored under a different prefix starting with log/. This specification may recognize additional conventions in later versions without invalidating existing files.

Name Type Size Units
:chunk:`log/particles/user_defined` n/a NxM user-defined
:chunk:`log/bonds/user_defined` n/a NxM user-defined
:chunk:`log/user_defined` n/a NxM user-defined
.. chunk:: log/particles/user_defined

    :Type: user-defined
    :Size: NxM
    :Units: user-defined

    This chunk is a place holder for any number of user defined per-particle
    quantities. *N* is the number of particles in this frame. *M*, the data
    type, the units, and the chunk name (after the prefix ``log/particles/``)
    are user-defined.

    .. versionadded:: 1.4

.. chunk:: log/bonds/user_defined

    :Type: user-defined
    :Size: NxM
    :Units: user-defined

    This chunk is a place holder for any number of user defined per-bond
    quantities. *N* is the number of bonds in this frame. *M*, the data type,
    the units, and the chunk name (after the prefix ``log/bonds/``) are
    user-defined.

    .. versionadded:: 1.4

.. chunk:: log/user_defined

    :Type: user-defined
    :Size: NxM
    :Units: user-defined

    This chunk is a place holder for any number of user defined quantities. *N*,
    *M*, the data type, the units, and the chunk name (after the prefix
    ``log/``) are user-defined.

    .. versionadded:: 1.4

State data

HOOMD stores auxiliary state information in state/* data chunks. Auxiliary state encompasses internal state to any integrator, updater, or other class that is not part of the particle system state but is also not a fixed parameter. For example, the internal degrees of freedom in integrator. Auxiliary state is useful when restarting simulations.

HOOMD only stores state in GSD files when requested explicitly by the user. Only a few of the documented state data chunks will be present in any GSD file and not all state chunks are valid. Thus, state data chunks do not have default values. If a chunk is not present in the file, that state does not have a well-defined value.

Note

HOOMD-blue >= v3.0.0 do not write state data.

Name Type Size Units
HPMC integrator state      
:chunk:`state/hpmc/integrate/d` double 1x1 length
:chunk:`state/hpmc/integrate/a` double 1x1 number
:chunk:`state/hpmc/sphere/radius` float NTx1 length
:chunk:`state/hpmc/sphere/orientable` uint8 NTx1 boolean
:chunk:`state/hpmc/ellipsoid/a` float NTx1 length
:chunk:`state/hpmc/ellipsoid/b` float NTx1 length
:chunk:`state/hpmc/ellipsoid/c` float NTx1 length
:chunk:`state/hpmc/convex_polyhedron/N` uint32 NTx1 number
:chunk:`state/hpmc/convex_polyhedron/vertices` float sum(N)x3 length
:chunk:`state/hpmc/convex_spheropolyhedron/N` uint32 NTx1 number
:chunk:`state/hpmc/convex_spheropolyhedron/vertices` float sum(N)x3 length
:chunk:`state/hpmc/convex_spheropolyhedron/sweep_radius` float NTx1 length
:chunk:`state/hpmc/convex_polygon/N` uint32 NTx1 number
:chunk:`state/hpmc/convex_polygon/vertices` float sum(N)x2 length
:chunk:`state/hpmc/convex_spheropolygon/N` uint32 NTx1 number
:chunk:`state/hpmc/convex_spheropolygon/vertices` float sum(N)x2 length
:chunk:`state/hpmc/convex_spheropolygon/sweep_radius` float NTx1 length
:chunk:`state/hpmc/simple_polygon/N` uint32 NTx1 number
:chunk:`state/hpmc/simple_polygon/vertices` float sum(N)x2 length

HPMC integrator state

NT is the number of particle types.

.. chunk:: state/hpmc/integrate/d

    :Type: double
    :Size: 1x1
    :Units: length

    *d* is the maximum trial move displacement.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/integrate/a

    :Type: double
    :Size: 1x1
    :Units: number

    *a* is the size of the maximum rotation move.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/sphere/radius

    :Type: float
    :Size: NTx1
    :Units: length

    Sphere radius for each particle type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/sphere/orientable

        :Type: uint8
        :Size: NTx1
        :Units: boolean

    Orientable flag for each particle type.

    .. versionadded:: 1.3

.. chunk:: state/hpmc/ellipsoid/a

    :Type: float
    :Size: NTx1
    :Units: length

    Size of the first ellipsoid semi-axis for each particle type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/ellipsoid/b

    :Type: float
    :Size: NTx1
    :Units: length

    Size of the second ellipsoid semi-axis for each particle type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/ellipsoid/c

    :Type: float
    :Size: NTx1
    :Units: length

    Size of the third ellipsoid semi-axis for each particle type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_polyhedron/N

    :Type: uint32
    :Size: NTx1
    :Units: number

    Number of vertices defined for each type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_polyhedron/vertices

    :Type: float
    :Size: sum(N)x3
    :Units: length

    Position of the vertices in the shape for all types. The shape for type 0 is
    the first N[0] vertices, the shape for type 1 is the next N[1] vertices, and
    so on...

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_spheropolyhedron/N

    :Type: uint32
    :Size: NTx1
    :Units: number

    Number of vertices defined for each type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_spheropolyhedron/vertices

    :Type: float
    :Size: sum(N)x3
    :Units: length

    Position of the vertices in the shape for all types. The shape for type 0 is
    the first N[0] vertices, the shape for type 1 is the next N[1] vertices, and
    so on...

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_spheropolyhedron/sweep_radius

    :Type: float
    :Size: NTx1
    :Units: length

    Sweep radius for each type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_polygon/N

    :Type: uint32
    :Size: NTx1
    :Units: number

    Number of vertices defined for each type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_polygon/vertices

    :Type: float
    :Size: sum(N)x2
    :Units: length

    Position of the vertices in the shape for all types. The shape for type 0 is
    the first N[0] vertices, the shape for type 1 is the next N[1] vertices, and
    so on...

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_spheropolygon/N

    :Type: uint32
    :Size: NTx1
    :Units: number

    Number of vertices defined for each type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_spheropolygon/vertices

    :Type: float
    :Size: sum(N)x2
    :Units: length

    Position of the vertices in the shape for all types. The shape for type 0 is
    the first N[0] vertices, the shape for type 1 is the next N[1] vertices, and
    so on...

    .. versionadded:: 1.2

.. chunk:: state/hpmc/convex_spheropolygon/sweep_radius

    :Type: float
    :Size: NTx1
    :Units: length

    Sweep radius for each type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/simple_polygon/N

    :Type: uint32
    :Size: NTx1
    :Units: number

    Number of vertices defined for each type.

    .. versionadded:: 1.2

.. chunk:: state/hpmc/simple_polygon/vertices

    :Type: float
    :Size: sum(N)x2
    :Units: length

    Position of the vertices in the shape for all types. The shape for type 0 is
    the first N[0] vertices, the shape for type 1 is the next N[1] vertices, and
    so on...

    .. versionadded:: 1.2